It's possible to kill everything if you have a lot of luck early on and a little luck later. The right level combinations (namely those that allow you to gift-drop most enemies) with a healthy number of globes get you to the point where you can start zerking effectively. Here's a [E|YAAM] fist run I managed about a month back. I recall the last levels being really annoying when dealing with Viles, but the MBm path makes it fairly easy getting to the VMR packs without taking too much damage. Malek's Armor helped a lot too, although nanofiber red was working before then.
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DoomRL (v.0.9.9.3) roguelike post-mortem character dump
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Game Hunter, level 11 Mancubus 1st Lieutenant, defeated the Cyberdemon
on level 25 of the Phobos base.
He survived 43310 turns and scored 49764 points.
He played for 37 minutes and 11 seconds.
He was too young to die!
He killed 418 out of 418 hellspawn. (100%)
This ass-kicking marine killed all of them!
-- Special levels --------------------------------------------
Levels generated : 7
Levels visited : 5
Levels completed : 5
-- Awards ----------------------------------------------------
Medal of Prejudice
Sunrise Iron Fist
UAC Star (bronze cluster)
Aurora Medallion
-- Graveyard -------------------------------------------------
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-- Statistics ------------------------------------------------
Health 50/80 Experience 50504/11
ToHit Ranged +0 ToHit Melee +6 ToDmg Ranged +0 ToDmg Melee +9
-- Traits ----------------------------------------------------
Ironman (Level 3)
Hellrunner (Level 2)
Brute (Level 3)
Berserker (Level 1)
Dodgemaster (Level 1)
Blademaster (Level 1)
Bru->Bru->Bru->Ber->HR->HR->MBm->Iro->DM->Iro->Iro->
-- Equipment -------------------------------------------------
[a] [ Armor ] Malek's Armor [1/3] (40%)
[b] [ Weapon ] nothing
[c] [ Boots ] tactical boots [1/1] (100%)
[d] [ Prepared ] rocket launcher (6d6) [0/1]
-- Inventory -------------------------------------------------
[a] modified blaster (2d5) [20/20] (P1)
[b] blue armor [2/2] (100%)
[c] Cybernetic Armor [7/7] (100%)
[d] Lava Armor [6/6] (100%)
[e] Berserker Armor [0]
[f] large med-pack
[g] large med-pack
[h] large med-pack
[i] large med-pack
[j] phase device
[k] homing phase device
[l] envirosuit pack
[m] thermonuclear bomb
[n] thermonuclear bomb
[o] bulk mod pack
[p] bulk mod pack
[q] shockwave pack
-- Kills -----------------------------------------------------
44 former humans
56 former sergeants
15 former captains
53 imps
44 demons
124 lost souls
16 cacodemons
17 barons of hell
1 Cyberdemon
4 hell knights
16 arachnotrons
6 former commandos
2 pain elementals
5 arch-viles
2 mancubi
10 revenants
2 bruiser brothers
1 lava elemental
-- History ---------------------------------------------------
He started his journey on the surface of Phobos.
On level 6 he assembled a tactical boots!
On level 6 he stormed the Chained Court.
On level 11 he ventured into the Halls of Carnage.
On level 14 he ran for his life from acid!
On level 15 he encountered the Phobos Hellgate.
On level 17 he found the City of Skulls.
He wiped out the City of Skulls.
On level 18 he assembled a nanofiber armor!
On level 19 he found the Malek's Armor!
On level 19 he ventured into the Spider's Lair.
He cleared the Lair, kickin' serious spider ass!
On level 20 he found the Lava Armor!
On level 22 he found the Cybernetic Armor!
On level 23 he entered the Lava Pits.
On level 23 he found the Berserker Armor!
He managed to clear the Lava Pits completely!
Then at last he found Phobos Arena!
On level 25 he finally defeated the Cyberdemon.
-- Messages --------------------------------------------------
You see : a Cyberdemon (wounded) [m]ore | floor
You hit the Cyberdemon. The Cyberdemon hits you.
You hit the Cyberdemon. The Cyberdemon hits you. You feel vulnerable again.
You start running!
You hit the Cyberdemon. The Cyberdemon hits you. Your Malek's Armor is
damaged!
You hit the Cyberdemon. You feel like a killing machine! You're going
berserk! The Cyberdemon hits you. You need to taste blood!
You hit the Cyberdemon. The Cyberdemon hits you. You need to taste blood!
You hit the Cyberdemon. You need to taste blood!
You hit the Cyberdemon. The Cyberdemon hits you. You need to taste blood!
You hit the Cyberdemon. The Cyberdemon hits you. You need to taste blood!
You hit the Cyberdemon. You need to taste blood!
You hit the Cyberdemon. The Cyberdemon hits you. You need to taste blood!
You hit the Cyberdemon. The Cyberdemon dies. You feel relatively safe
now. Congratulations! You defeated the Cyberdemon! Press <Enter>... Next!
-- General ---------------------------------------------------
Before him 62 brave souls have ventured into Phobos:
51 of those were killed.
And 2 couldn't handle the stress and committed a stupid suicide.
Some rumours though, say that the Cyberdemon was killed already!
Is he immortal? 9 souls claim to have killed him...
2 sacrificed itself for the good of mankind.
7 killed the bastard and survived.
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Regarding your game:
I decided to just take the Hellrunner path instead of trying to go straight for Berserker, since I was taking way too much damage early game just to get by. Some people like to take Tough as Nails in this situation though, so I'm not sure which is generally better in this kind of run.
Because of the double healing factor in ITYTD and N!, many agree that MBm is preferred. For the most part, it depends on what master you'd be aiming for in the long run. Vampyre supplements a melee run in that it gives you a fighting chance while unzerked (healing off of easier enemies, damage reduction) while Blademaster complements the zerking aspect in that you kill instantly (which gives free turns of zerk).
Somewhere in between the start and Hellgate, I manage to pick up an agility mod and used it immediately on my boots for a much needed speed boost. Since I'm taking the speed path I was aiming for enough speed to outrun demons as they're big trouble if I get spotted by them. In the next level I found a shockwave pack near the entrance and this was an extremely vital item in this run. I was glad to at least have it.
Just as a heads-up, you CAN use any weapon in a fist-only or similar challenge, you just can't KILL anything with those weapons. To this extent, picking up a rocket launcher for wall-blasting or rocket-jumping can be vital for these kinds of runs, particularly as you make your way to Strongman Platinum/Diamond. I'm mentioning it here because this is how I picked up the agility mods at CC in the run posted at the top.
Encountered two nukes on the stairs
back-to-back, but thankfully the stairs weren't too far apart.
Depending on your state, it may have proved worthwhile to search for invulnerability globes on those levels. If you find one, it's very possible to wait out the nuke and reap the experience from all enemies being destroyed on the map.
Sounds like a real struggle against the Cyberdemon (but those are the most fun ones!) and glad to see you made it through in spite of the odds against you. As for the Strongman series (or at least starting with Gold), it's REALLY difficult to pull off. In many ways it's like Angel of Pacifism, although you lack the auto-leveling. Given the scaling, you either need to be lucky enough to level often in the early stages or lucky enough to glide past the stairs, snag the Mort nuke, and clean house. Not many have picked those badges up past the Gold, even.