Hey there, NeonBuddha, I was just replying to your comment on Discord when I noticed this thread and decided I should probably post here instead. :)
It looks like you were doing really well this game! (And with Gunrunner! Interesting choice! How do you find it? I find people have mixed opinions of it) You had a really good collection of supplies and had done a good job of clearing every special level up to this point. (Was this really your first game? Or was this a re-install or something?) ...But Unholy Cathedral is a totally different animal... If you're trying to do a Conqueror run, you have to devote some unusual planning to deal with this particular level and, unfortunately, it looks like you were unprepared in this case.
You asked about this level on Discord, and I outlined possible strategies, so to recap: You had no Berserker trait, (no Brute even!) no Hatred skulls, no Combat Knives, no Anti-gravity boots, no Ripper, none of the things that would allow you to defeat the Angel of Death, the major boss of this level. I don't know if you've faced him before, but the AoD is tough, *really* tough. Heavily armoured, deals high melee damage, and is fast! You had no Ironman, no Tough as Nails, and your armour was shredded, so if you had tried to go toe-to-toe with him, those medpacks would be gone really fast and you would be lucky to "lightly wound" him. (Having armour that conveys melee protection is a big help, like Ballistic vest/shield and/or the Ballistic armour assembly)
Beyond that, I think it's also worth pointing out that you didn't have to face those Demons directly; you were fast enough to outwalk them, so you could have led them into a lava bath outside the cathedral. You don't even need to step in the lava; just walk around the pool while they're chasing you and they'll die in the lava as they try to cross it to get to you. (Though if you're using the Hatred skull strategy, you'll still want to kill a few of them outside the lava so you have corpses to power it)
Hope this helps! And I'm sure you'll do better next time; you clearly have some skill. :)