EDIT: I've updated many parts of this post as I've gone from theorycrafting to actually playing runs and also achieving the badge. A lot of information is improved.
Everyman Angelic Badge is an extremely difficult challenge and it's very unique in many ways that I find really interesting and exciting. As hard of a badge it is to earn, the initial build selection and planning is very simplified compared to normal gameplay because of the lack of traits. With Nightmare difficulty, 10 base maximum HP, and only one trait, you are very limited in what you can do and what you're capable of, which also makes it much easier to optimize, or at least hypothetically. With this in mind, the one trait you do select and how it impacts every part of the game is very critical, so it's worthwhile analyzing all of the possibilities.
Class Choice
Between the 3 classes who each have 10 traits, there are effectively only 30 builds, compared to the functionally infinite ways to make a build for normal games. Since the traits are all the same across the classes except the starting advanced trait available, the first part is to analyze each class. Hypothetically, most traits could be used to get a completion, and very hypothetically, all of them could, but the focus is on which is the best for the purposes of human realism on getting a completion.
Scout
Scout has 10% more speed than other classes inherently, which negates the speed loss from Nightmare difficulty, overall still being faster than other builds and also helping simplify some calculations. Of course, the main perk out of a Scout is stair sense. Given that your character will be a complete wimp, any sort of attempt of clearing out floors would be pretty much impossible, and it's ideal to be diving to the stairs, only detouring for items such as Invulnerabilities. Since level-ups have no effect, killing enemies offer no benefit besides their drops, so clearing out everything is unnecessary and dangerous. This makes stair sense incredibly important for success by reducing the exploration time down to a fraction compared to those without stair sense.
Marine
On Nightmare difficulty, each Invulnerability and Berserk offers 100 actions of duration, and a Marine has 125 instead. While the extra turns are certainly helpful, it's not as strong of a boost on Nightmare difficulty, and compared to stair sense, those 25 extra turns will likely just get burned through trying to find the stairs. The Marine also has 12 HP as opposed to 10, but unless your total damage taken is hitting 10 or 11, it's likely not significant enough of a benefit. The Marine's Badass trait helps preserve more HP up to 18, but that's an expensive trade-off for the boosts in speed and power. You can't be taking too much damage in general, so having extra health to burn won't be saving you from too much extra in the late game, and you can probably reduce damage taken by stopping enemies easier with other traits. The Marine doesn't seem to offer anything to be worth choosing over Scout.
Technician
The Technician comes with many various perks, but most will not significantly help survive through this challenge. Computer Maps functioning as Tracking Maps can help you avoid enemies, but you likely won't find too many while specifically not finding a Tracking Map per game, and they may simply just provide you with confirmation that you're about to die. They do offer the only way to see enemies since Intuition 2 is unavailable, but any class can likewise find Tracking Maps. Modifying a few unique items is pretty useless as they're all very rare, the perk only slightly improves them, and you have to first get far enough into the game for them to even be able to appear. Instant item use is a very good perk however as you're able to immediately heal without being instantly attacked and having your health brought back down. This helps a lot with reducing burning through Med Packs, but is likely still not outclassing stair sense. With Whizkid 1, it opens up quite a few useful assemblies such as Focused Double Shotgun and Hyperblaster, and it's possible to farm ammo for both, so I wouldn't write-off using it, especially starting off with plenty of Mod Packs to immediately make either if you find the corresponding base, but using a Hyperblaster is arguably not better than a much faster Scout using a Plasma Rifle and diving for the stairs. With no supportive traits, Focused Double Shotgun is still fairly dangerous to use with its slow reload time, and Hyperblaster will still be burning through ammo and needs a support weapon. Even with them, you likely won't be able to reasonably fend off the huge numbers of enemies.
Likely unsurprising, Scout is the class of choice, but I do think a Technician or Marine could possibly get through too if they find correspondingly beneficial items. Stair sense is just far too useful and the speed boosts help allow you to reduce damage and clear paths by simply being able to kill enemies easier as they approach.
Trait Choice
Next is to break down the Scout's trait to select.
Ironman
Ironman adds 20% of your base maximum health, which in the case of Archcangel of Humanity is only 2. As is often the case in normal games, it's a bit of a filler trait and the negligible increase in health likely won't make a significant difference in your survivability. It's much more beneficial to simply be faster and reduce the possibilities of taking damage in the first place, rather than having extra health as a crutch. The only niche it's useful for is that Trigun's Angel Arm can't be used unless you have at least 11 maximum health, but finding it, burning off those extra 2, and not having another trait is all not worth having a free nuke.
Finesse
Finesse gives you a nice boost to firing speed, which can greatly help support the Shotgun's slowish speed and give you much more opportunity to keep enemies away. If you start in an open area with multiple fronts, it also helps a lot with pushing back more enemies in at a faster rate. This all said, 15% is only on average saving you an action for every 7 shots and doesn't help with reloading, so the speed increase isn't gigantic. It does also help with using the Chainsaw on the Cyberdemon if you don't have Invulnerability because you will get hit back slightly less often. If you like to throw in the starting Bulk Pack into a Shotgun for faster reloading speed, naturally having faster firing speed also helps smooth out your overall speed with using a Shotgun, instead of a small spike and large spike between firing and reloading. Overall, it helps a fair bit throughout the whole game and is one of the better choices.
Hellrunner
Providing 15% movement speed is very helpful for a game that will be focused on stair diving, and the dodge bonus is also helpful, both for regular levels, and often the Cyberdemon as well. To nitpick, compared to other traits, it won't help at all when standing in place and firing at enemies, and because Invulnerability and Berserk are based on movement actions, Hellrunner results in burning more turns to get to the Cyberdemon since it will be moving less often as you charge it. The other critiques against it is that because a completion of this challenge will likely be the result of stacks of Berserk and Invulnerability, Hellrunner isn't really helping under optimal situations, but of course is much more helpful when you have worse luck and have to run through without power-ups. Hellrunner is likely one of the choices, since traits that help combat are a bit irrelevant with how fruitless fighting back often is, but because of the dynamics and infinite possibilities, there may be many cases where others are better.
Tough as Nails
Tough is Nails isn't honestly terrible, since even reducing damage from 2 to 1 effectively doubles your lifespan, but it's a rather passive trait instead of something proactive. In order for it to save you from death, the sum of damage reduction has to equal the damage of an attack that would have otherwise killed you, which often is only giving you a couple extra hits across multiple floors if even that. It does help a lot more in the early game where damage is a lot lower, so I wouldn't completely write it off, but it's certainly not the most beneficial trait.
Son of a Bitch
Adding on an extra bit of damage to everything is nice, but it only helps if the 1 point difference saves you a shot or more per kill. Granted, this amount could be a lot, but would be hard to determine just how much Son of a Bitch is helping. Shotguns are fairly weak from a distance, which you may find yourself doing a lot, so that extra bit could be reducing the required shots by a lot in some situations, especially for tough enemies. The main comparison is if the faster kills are reducing the number of hits to simply being able to fire back faster with Finesse. More knockback with Son of a Bitch can also help slightly. Overall, I think it could be decent, but I don't think it's a top pick overall.
Son of a Gun
Given the nature of this challenge, you don't want to be using pistols. Pistols are only good with a full build dedicated to them, and a single trait is nowhere near enough to justify using them.
Reloader
Reloader is normally a pretty underwhelming trait, but because of the huge reliance on Shotguns and the better speed improvement compared to Finesse, it helps save a bit extra time, although is less helpful for other weapons. Reloader with the Bulk Pack in Shotgun gives the fastest speed for the beginning of the game, but is a bit spiky as firing speed isn't improved, and the Technical Pack helps smooth out shooting better. Reloader is definitely the best trait in terms of attacking in place with a Shotgun, but is a fair bit worse than other traits in most other situations. A lucky Shell Box also negates most of the benefits of Reloader, as opposed to Finesse which doesn't have a simple replacement.
Eagle Eye
Given that Shotguns are the most effective weapon without traits boosting them, Eagle Eye is likely not a great pick since they don't help them. The main appeal is it does somewhat open up using other weapons such as a Chaingun that goes from 74% accuracy to 91% accuracy at point blank. With the huge onslaught of enemies though, Shotguns are more helpful with groups and are also more ammo efficient, but a Chaingun could help with single targets or if you need to use several bursts without the risk of using reload repeatedly with a Shotgun. The Chainsaw and Plasma Rifle also enjoy increases to accuracy, which would help a lot for the Cyberdemon and Spider Mastermind. I think Eagle Eye could be usable, but I don't think it's the best choice with how much Shotgun should be used and that running through floors to the stairs tends to be a more effective strategy anyway.
Brute
It should go without saying that melee is not the way through this challenge. The main perk out of Brute is it can help speed up the Cyberdemon fight while Invulernable and/or Berserk, moreso because of the accuracy increase, but it's not really helpful at all for the rest of the game. Even with a miraculous Dragonslayer or Butcher's Cleaver, the hits you'll be taking even while camping are way too much for your tiny health amount.
Intuition
Intuition is a bit gimmicky in that it doesn't directly improve your character at all and simply informs you of where useful power-ups are, but because Invulnerabilities are essentially critical for success, I personally believe Intuition is the best build to use. The slight perk of knowing what levers may do isn't a huge deal, but can be slightly helpful for quick heals and armor repair. For Intuition to be beneficial, it has to influence your decision-making on where you go in a positive way, such as showing you that an Invulnerability or Berserk is a little further past the stairs, or nearby the opposite direction at the start. Knowing where healing power-ups is also helpful as you will likely need to rely on them to survive. However, the big setback is that Invulnerabilities only appear starting on floor 7 of Phobos, which makes Intuition a lot less useful early on. It's still great for Berserk Packs and Health Globes, but other traits are definitely better with getting through Phobos. Under ideal situations with lots of helpful power-ups, Intuition is the best, but Hellrunner is generally better in less than ideal scenarios. While getting through Phobos is hard, a player can definitely grind out runs through it and then hopefully find stacks of Invulnerabilities for an easy walk through the rest of the game.
With all of these choices and widely varying circumstances, it's difficult to determine which one is the best overall, but I would argue Intuition is the best choice by a fair-sized gap. Getting through Phobos will require more skill and more luck, but the potential to make the rest of the game as easy as possible with this challenge is such a huge benefit. Hellrunner is definitely the second best choice by providing the very helpful movement speed and dodging bonus to escape each floor, and will always be beneficial, instead of Intuition which is not as consistent. The next tier down by a fair gap would likely be Finesse and Reloader, followed by Son of a Bitch and Eagle Eye. The other 4 traits definitely are outclassed, and using a Marine or Technician is definitely also outclassed. This overall leaves 6 build choices that are at least somewhat viable, but I would strongly recommend Intuition.
Mod Pack Usage
Next is some planning for the run itself.
As you start with one of each Mod Pack, good use of them is important. The Bulk Pack could contribute to either reducing Shotgun reloading time by 25%, or giving the Chainsaw a damage buff. Damage calculations later will show that Piercing Blade isn't often worth using and Chainsaw (B) is very strong. High Power Weapon and Gatling Gun are generally outclassed by Shotgun, unless you're using an Eagle Eye build, so I think the best use of the Bulk Pack is the Chainsaw and using the Technical Pack for the Shotgun instead.
The Agility Pack can be immediately used in your starting Red Armor as it offers a 15% increase in speed compared to 10% in boots that you may not find right away. The Power Pack on the other hand gives 2 extra protection to Red Armor, and since you don't have much health to begin with, the durability of the armor should last a long while to make good use of it. Below are some damage calculations (I believe I have the rounding calculated correctly):
Former Human pistol shot vs Red Armor: 2d4 - 4
6.25% for 4 damage
12.5% for 3 damage
18.75% for 2 damage
62.5% for 1 damage
Former Human pistol shot vs Red Armor (P): 2d4 - 6
6.25% for 2 damage
93.75% for 1 damage
Former Sergeant shotgun blast (1 tile distance) vs Red Armor: (8d3 - 14%) - 8
2.39% for 10 damage (dead without health boost)
4.05% for 9 damage
7.68% for 8 damage
27.44% for 7 damage
16.87% for 6 damage
15.49% for 5 damage
11.95% for 4 damage
7.68% for 3 damage
4.05% for 2 damage
2.39% for 1 damage
Former Sergeant shotgun blast (1 tile distance) vs Red Armor (P): (8d3 - 14%) - 12
0.02% for 9 damage
0.12% for 8 damage
0.55% for 7 damage
1.71% for 6 damage
4.05% for 5 damage
7.68% for 4 damage
27.44% for 3 damage
16.87% for 2 damage
41.56% for 1 damage
Imp fireball vs Red Armor: (2d5 - 25%) - 4
4% for 4 damage
8% for 3 damage
12% for 2 damage
76% for 1 damage
Imp fireball vs Red Armor (P): (2d5 - 25%) - 6
4% for 2 damage
96% for 1 damage
Demon melee attack vs Red Armor: 1d3 + 5 - 4
33.33% for 4 damage
33.33% for 3 damage
33.33% for 2 damage
Demon melee attack vs Red Armor (P): 1d3 + 5 - 6
33.33% for 2 damage
66.67% for 1 damage
As you can see at a glance, Red Armor (P) significantly helps reducing damage in the early game. Whether or not that it makes up for the 15% speed increase with Red Armor (A) is far too complex of a question to answer, but given that you can find Steel Boots early and still come with 10% speed, I think it's most reasonable to use the Power Pack for Red Armor. If you find a second Agility Pack, it may be better to put into the Phobos Anomaly Red Armor as Tactical Boots only gets 5% extra speed as opposed to 15% for armor.
The Technical Pack is best used for a weapon, which can be either Shotgun, Combat Shotgun, or possibly Plasma Rifle, although I would suggest Shotgun. If you want to use the Bulk Pack for Chainsaw for more damage, then the Technical Pack fits well into the Shotgun. You could also use the Technical Pack for the Chainsaw to increase attacking speed, although this only gives about 1 extra hit per 5 against the Cyberdemon and is not terribly beneficial compared to more damage. The best use may instead be simply holding onto it in the case you find a Combat Shotgun.
To summarize, I think the best application is:
Shotgun (T), Red Armor (P), Steel Boots (A), Combat Shotgun, Chainsaw (B)
Alternatives include:
Shotgun, Red Armor (P), Steel Boots (A), Combat Shotgun (T), Chainsaw (B)
Shotgun, Red Armor (A), Steel Boots, Tactical Shotgun, Chainsaw (B)
Shotgun (T), Red Armor (A), Steel Boots, Combat Shotgun (P), Chainsaw (B)
Shotgun (B), Red Armor (P), Steel Boots (A), Combat Shotgun (T), Chainsaw
Shotgun (B), Red Armor (A), Steel Boots, Combat Shotgun, Chainsaw (P)
Which is best will highly vary based on what Mod Packs you find, how early you find boots and a Combat Shotgun, playstyle, and also what trait you picked.
Phobos
Phobos Base Entry is best played by taking cover at one of the corners of the building, grabbing a Shotgun as safely as possible, and then preventing corpses from respawning. This can be done by stacking them on top of each other, shooting enemies into the outer edges, or simply standing on them while clearing out others. Keep health as high as possible, try to one shot kill enemies in order to get the extra Small Med Packs, and be sure to exit with large stacks of shells. Keep a few open slots as you may find items worth grabbing later and don't want to spend time dropping garbage.
Because most enemies will make quick work of you in Deimos and Hell, you don't have time to heal later, and Phobos Anomaly itself has two Large Med Packs, it's important to not be stingy with using them throughout the floors of Phobos. It's much better to have a below average run than to risk dying, since both a good or bad run essentially need the same type of luck in Deimos and Hell anyway. Work your way to the stairs as safely as you can on each floor and be sure to take shots into open, dark areas to scout for enemies. Phobos 3, 4, and 5 get dangerous fast with Hell Knights and other enemies, and The Chained Court is essential for success because of Berserk Packs and the Chainsaw. It can be a bit demotivating to spend time getting a good start through Phobos Base Entry only to die quickly after, so you'll need to tough things out and keep grinding for runs.
For multi-hit enemies such as Former Captains, Former Commandos, and Arachnatrons, who all can quickly melt your health, it's often safer to lure them in around cover and attack with Chainsaw. Damage reduction does bring their shots down in power, but the quantity of them is too high to survive for long.
Phobos Anomaly
Next is analyzing how to get through Phobos Anomaly.
Phobos Anomaly gives a fresh Red Armor, two Large Med Packs, and enough health to be at a maxed 20% as you enter the trap. The easiest way to get through is a fortunate floor 7 Invulnerability, which is the first floor it can spawn on. Otherwise, using either type of phase device to hopefully get past the trap or rocket jumping through with a Rocket Launcher. Even with any kind of support, Hellrunner helps significantly with the faster movement speed and the extra dodge bonus chance. Intuition is useless for this floor. There aren't really too many safe ways to be killing any enemies, so any of the other possible traits to pick aren't helpful here. Ultimately, this level will be a barrier for many games.
Nightmare Demons will uniformly do damage in the range of 11-13, so even with 200% HP and Red Armor, you can only survive 2 hits, but you can definitely be killed in just 2 after health decay and high damage rolls. Nightmare Cacodemons will do an average of 6 damage after considering Red Armor protection per plasma ball, which also can't be tanked for very long. Finally, while Nightmare Imps do an average of 5 damage after protection per plasma ball, they more importantly can open doors so you aren't able to camp in the first or third room. Because of all this, you'll have to simply run through, and you are essentially forced to grab all of the Berserk Packs from The Chained Court. With all 4 and the Chainsaw, you'll have 500 turns of Berserk, which functionally guarantees you Berserk at Phobos Anomaly and significantly reducing all the damage, almost entirely down to just 1. Unless you have a horrendous floor 6 and 7, or have no choice but to spend time firing at enemies, you should be able to be Berserk every run through Phobos Anomaly. There is just no other way to get through Phobos Anomaly with any amount of consistency.
For the Bruiser Brothers, rocket jumping between them is the fastest way through and helps avoid damage the most, but otherwise pick a side and run by. Being near them will increase the chance of being hit, but being near the wall will lead to getting caught in the splash damage. Take a note of where the plasma balls will hit in the case of a miss for each movement, and move in such a way to avoid the splash damage. Depending on the angle and positioning, you could attempt to get hit by the end radius and use the damage to be knocked back further ahead, but this needs to be done precisely. You may prefer just getting hit by melee attacks, which will keep your armor's durability higher, and will only do 1 damage assuming you have Red Armor. Regardless of what support you have, always get to the teleporter as fast and safely as possible. You'll likely get destroyed many games on this level if you don't have Berserk Packs.
Tower of Babel
The Cyberdemon has 450 health, its melee damage ranges 16-18 uniformly before reductions, and rockets will do huge chunks of damage if not outright kill you without protection through Red Armor and/or Berserk. Ideally, you'll have had more opportunities to be Invulnerable and/or Berserk and be able to be powered up for Tower of Babel. Hellrunner is a bit disadvantageous for charging to the Cyberdemon as the duration for power-ups is turn-based and the Cyberdemon will be moving a bit less each turn. Even with Hellrunner's dodge bonus and with max distance away, the Cyberdemon's health is far too high to chip away at with a Shotgun without eventually getting hit, so using the Chainsaw is the only way to go, but if you're not Invulnerable, you must absolutely be Berserk as the melee damage back is way too high. In the case you have a nuke and are Invulnerable, immediately blowing up the level is the best use as the Spider Mastermind can be killed much easier.
Given 450 health and 4 armor, the following are some damage calculations for different types of Chainsaw. All calculations assume being Berserk.
Chainsaw: 4d6 x2, average damage of 24, average of 18.75 hits to kill, average of 37.5 attacks to kill.
Chainsaw (A): 4d6 x2, average damage of 24, average of 18.75 hits to kill, average 30.24 attacks to kill.
Chainsaw (B): 5d6 x2, average damage of 31, average of 14.5 hits to kill, average of 29.03 attacks to kill.
Chainsaw (P): 4d7 x2, average damage of 28, average of 16.07 hits to kill, average of 32.14 attacks to kill.
Piercing Chainsaw: 4d7 x2, average damage of 32, average of 14.06 hits to kill, average of 28.13 attacks to kill.
Eagle Eye + Chainsaw: 4d6 x2, average damage of 24, average of 18.75 hits to kill, average of 25.34 attacks to kill.
Eagle Eye + Chainsaw (B): 5d6 x2, average damage of 31, average of 14.5 hits to kill, average of 19.59 attacks to kill.
Eagle Eye + Piercing Chainsaw: 4d7 x2, average damage of 32, average of 14.06 hits to kill, average of 19 attacks to kill.
At a quick glance, Eagle Eye significantly improves the fight, requiring far less hits. With Invulnerability, this saves an average of about 10 turns, helping you be sure you have enough entering, and more likely to have some duration after the kill. That said, I would argue it's not enough to justify using Eagle Eye over Intuition, Hellrunner, or other good traits for the game up to this point.
The other notable point is that Piercing Chainsaw is very overrated while Berserk, and doesn't reduce the fight by much. Because Berserk doubles damage before armor reduction, the piercing doesn't add too much extra damage compared to a simple Bulk Pack. When not Berserk, the 4 damage boost is a more significant percentage of damage, but you likely won't survive long without Berserk anyway. However, Piercing Chainsaw is certainly helpful if you have Invulnerability and no Berserk:
Chainsaw (B): 5d6, average damage of 13.5, average of 33.3 hits to kill, average of 66.6 attacks to kill.
Piercing Chainsaw: 4d7, average damage of 16, average of 28.13 hits to kill, average of 56.25 attacks to kill.
Because of this, it could be argued that Chainsaw (B) and Shotgun (T) is a much better initial setup, and that likewise gives extra viability to using Reloader for getting starts. Using both an Agility Pack and Power Pack for Chainsaw is a large investment and likely doesn't help as much as using them for other items.
In any case, Tower of Babel is very simple to play optimally in, but requires good luck to realistically survive.
Dis
To start, if you have a nuke, immediately use it and win the game.
If you have enough Invulnerability and Berserk, it's possible to simply charge at the Spider Mastermind and attack until you get the kill. Flinching is a bit uncommon due to missing half the hits and needing a high damage roll, so if you have no power-ups, do not go for melee attacks. While the Spider Mastermind's melee damage is puny, its AI is fairly unpredictable and if it moves too far away and fires, your health will get destroyed. Berserk and Red Armor can reduce many shots down to 1, but bursts of 4 are still dangerous. Without Invulnerability, it may be wise to go for getting the Spider Mastermind stuck at one of the middle pillars. Below are various damage calculations using Chainsaw, assuming Berserk:
Chainsaw: 4d6 x2, average damage of 26, average of 19.23 hits to kill, average of 38.46 attacks to kill.
Chainsaw (A): 4d6 x2, average damage of 26, average of 19.23 hits to kill, average 31.02 attacks to kill.
Chainsaw (B): 5d6 x2, average damage of 33, average of 15.15 hits to kill, average of 30.30 attacks to kill.
Chainsaw (P): 4d7 x2, average damage of 30, average of 16.67 hits to kill, average of 33.33 attacks to kill.
Piercing Chainsaw: 4d7 x2, average damage of 32, average of 15.63 hits to kill, average of 31.25 attacks to kill.
Eagle Eye + Chainsaw: 4d6 x2, average damage of 26, average of 19.23 hits to kill, average of 25.99 attacks to kill.
Eagle Eye + Chainsaw (B): 5d6 x2, average damage of 33, average of 15.15 hits to kill, average of 20.48 attacks to kill.
Eagle Eye + Piercing Chainsaw: 4d7 x2, average damage of 32, average of 15.63 hits to kill, average of 21.11 attacks to kill.
Once again, Piercing Chainsaw is very overrated, and in fact worse than Chainsaw (B). Eagle Eye also helps save many turns, but it's still likely too much of a disadvantage for the rest of the game to be worth getting an advantage for the fight here. With Berserk, so long as you hit, there's a good chance of getting a flinch, so if you have enough Med Packs, Red Armor, and Berserk, charging into the Spider Mastermind can be fine even without Invulnerability.
If you don't have any power-ups but plenty of ammo, the best strategy is to go to the corner of one of the pillars, watch where the Spider Mastermind goes, and slowly and safely have it go around so that you can run to one of the middle pillars. Once in place, stand at one of the spots that is one space away from the pillar and one space away from the wall. If the Spider Mastermind becomes visible on the other side, fire, and depending on how it tries to move, may get stuck and only be able to move vertically in a space of 3 tiles permanently so long as you stay in place. If so, you can simply shoot it to death without any danger of it going anywhere else or being able to hit you. If it doesn't get stuck and charges through, run around the other way. If the Spider Mastermind went back, you won't be able to distinguish whether it got stuck or just moved away due to lack of Intuition 2. Hellrunner is very helpful for going for this setup. If you're unfamiliar with this technique, practice it in an easier game first because it helps trivialize the fight, but requires some technical knowledge. If you're unfortunate with the setup, the Spider Mastermind can get dangerous, which is where Hellrunner helps a lot, but is possibly more unsafe than charging with a Chainsaw while Berserk. Even with perfect play, some bad luck and not getting it stuck can result in an unfortunate death.
Conclusion
Having achieved this badge and spending some time theorycrafting and testing things, I highly suggest using Intuition and grind runs past Phobos Anomaly until you eventually get the Invulnerabilities you need to make it through. Another key thing is Bulk Pack in Chainsaw is cheaper, and against the Spider Mastermind, actually better than Piercing Chainsaw. Not using Piercing Chainsaw also opens up use of any extra Power Packs or Agility Packs you find. This means the Technical Pack can go into the Shotgun instead. Agility Pack can go into either boots or armor, but I would argue that Red Armor (P) reducing damage is incredibly helpful with reducing early game damage. Alternatively though, Red Armor (A), also opens up Tactical Shotgun if you find Combat Shotgun.
Scout with Intuition seems to be the best choice overall, but Hellrunner is more consistently good with lower peaks. Reloader helps smooth out Shotgun attacking speed if it has a Technical Pack, but Finesse is more helpful for starting floors and Chainsaw usage, as well as if you find a Shell Box. There are some potential niche uses out of Eagle Eye and Son of a Bitch, but are definitely outclassed.