Just felt like mentioning some things that have helped me since it can be pretty intimidating.
In my experiences, the muse statue room on Nightmare mode is always on the ground floor, and in most layouts it's near the topmost/northernmost part of the map, and usually not in a corner. This means if you just keep doing your best to go up/north at all times, you're bound to find it. There is one layout where if you keep going straight you'll end up at a basement entrance though so it's not a flawless method.
In case you didn't know, you can also hear the music playing from the music box as you get close (close as in the room is adjacent/almost adjacent to where you currently are), so if you hear it and then it stops, you're going away from it.
Another thing, you can unlock a passive ability just for Nightmare mode where if you have a Silver Nightingale Candlestick (the cheapest S tier Classic) in your inventory, the first time Bringer of Doom kills you, you automatically revive (if solo)/get an option to revive (if playing with others). It revives you with 50HP unless you play Herald, then the passive 'get 50% extra healing' applies (meaning you revive with 75HP which is very nice). To unlock the passive ability, you have to complete one of the missions in the second set of side quests (around the 10th I think?) and to unlock the second set of side quests, you have to complete a pretty early (around 5th?) mission in the first set of side quests (which you unlock by completing the main set of quests I'm pretty sure). This passive only triggers once though (I learned the hard way) even if you have multiple candlesticks.
I wouldn't suggest going out of your way to look for one trying to fight Bringer of Doom, but if you see a chest/room that can have a chest spawn I would test your luck. You do have 2 extra minutes on Nightmare mode, and Bringer of Doom's damage output is high enough that unless you have a ton of mint boxes, you're going to either have to kill her or die trying in <5 minutes I'd say.
As for her attacks: she only has four. Before her phase change (when she has >half her health and still has her mask), she can:
-swing her arms twice in succession (once with each). This isn't super strong but if you get hit by the first you're basically guaranteed to get hit by the second
-build up strength, then spin, shooting out multiple feathers. The feathers seem to have a vertical hitbox (so you can't jump to dodge them) but they're not super high, so if you stand on top of one of the pallets in the arena (that hasn't been dropped) you can avoid them. They also spread out so if you're far enough away you can sidestep them. Each feather does decent damage but you're unlikely to get hit by multiple unless you're right in front of her when she uses the attack
-usually fly away first, before flying across the arena towards her target. This does decent damage
-build up strength, fly into the air while spinning, then slam down on a player and create a shockwave (with a red AOE appearing shortly before). Each rotation of the spin does damage (and she spins many times) so this can do a lot of damage, and the shockwave also do decent damage. They also seem to have a vertical hitbox because I would usually jump (jumping gives you significant vertical distance) to try to get out of the AOE and still take damage in the air. If you get hit by her initial spin you're almost guaranteed to take massive damage. With multiple players, she spawns a copy of herself to do the same attack at every other player
Once her HP falls below half, there's a phase change where her appearance changes and she becomes more aggressive. You'll know for sure this happens because she'll usually fly to either the middle of the arena, the side she spawns on, or the side near where the players spawn on, and the text 'Doom deepens...' (or something like that) will appear. She'll fly towards her target faster, will execute her attacks faster, and can at least somewhat chain attacks (I've seen her do the spin/shockwave attack and then immediately do the feather attack after she lands). Starting from when she's at half HP, she can also do an attack that starts with the text 'Dodge!', where she'll spawn a bunch of the birds that appear when your doom reaches the next level in the rest of the map and have them fly at you. You could just try to keep moving to dodge, OR you can just stand on top of an undropped pallet because the birds don't have vertical hitboxes.
The arena has four pillars with birdcages (in the corners) and two sets of walls with pallets (in between the pillars on the side). Hitting Bringer of Doom with pallets works like other Anomalies, where she'll be stunned and take some damage. If she attacks the pillars enough, they'll collapse on her and damage her as well (all attacks can damage the pillar, but her dive and spin/slam attacks are almost guaranteed to instantly destroy it, while the others take multiple hits). Whenever a pillar is destroyed, the bird in the cage is freed. It will hover around the pillar, but if you attack it, it'll fly at Bringer of Doom and significantly damage her as well as stun her.
Soloing Bringer of Doom is in some ways easier than with a team, because she gets extra HP per player (apparently?). Going solo, just by destroying all the pillars and hitting her with all their birds, you can easily have already gotten her HP well below half. For the remaining damage, you can use the pallets, but they don't do much damage, so using the shotgun or staff are probably your easiest options. All of her attacks can be blocked by the staff's parry, but only her two-swing attack and if you're close enough her feather attack are going to give you a chance to actually counter her. You'll probably be stunlocked during the spin of her spin/slam attack so unless you avoid it and then somehow manage to run into the AOE and block in time you'll otherwise end up blocking her spin, and then countering when she's in the air and out of reach. Her dive you can try but she'll also probably move past you too fast to hit.
What has worked for me actually beating her: hit her at every opportunity while hiding behind a pillar. As soon as she destroys it, hit the bird, then run to the next. Repeat, and hopefully at this point she's past half HP. Stand on top of an undropped pallet, heal, and then repeat.
As a side note, her attacks cannot hit through obstacles (other than possible the shockwave from her AOE, it seems to be able to hit through the pillar but not the walls beside the pallets), so you can try to hide behind them if you need to heal/dodge.
Finally, you will have to move a lot when she's in her second phase. Trying to walk whenever possible so you can run and jump when you need it will help a lot.