*This guide is based on having Super Costumes*
Alright so, you can select Bloody Palace from the main menu. It's a place where enemies come in waves. It has 101 stages. If you die, you will need to restart from stage 1 so I suggest play with patience and don't get yourself killed and waste your time. after completing a stage, you can use "Suspend" in the pause menu to save your progress and quit to the main menu. so you don't have to go through all 101 stages in one go.
there is a boss fight at every 20 stages. so there is a boss at stage 20, 40, 60, 80. near the end, the algorithm changes and you'll get a boss fight at stage 90, 98,99,100,101. stage 101 is the hardest, obviously. normally you'll receive health before boss stages but you have to do stage 98,99 and 100 with the same health bar. then you'll receive health for the last stage. I suggest finishing the game on Dante must die to receive Super Costume. bear in mind that the Unlimited Devil trigger WON'T heal you. If you die somewhere, before starting again you can select "Warm up". and it allows you to practice the last stage that you died in and all the other stages before it.
Obviously, Nero is the hardest to complete BP with. but unlike others, his real threat is Urizen stage 98,99 and 100. the annoying thing is you have to go through all the 3 stages with the same health. I suggest practicing these fights in the story missions and learn his moves. as for the Devil Breakers, stack up Punch line (for Vergil) and Ragtime. (for Urizen) Other stages are not really a problem If you are familiar with the enemies. try not to risk losing your Ragtimes for Fury enemies. use Gerbera and spam B in any direction until you hit them.
when you stun Urizen or hold and release B to stop time with Ragtime, then use Showdown( DT active, LS+ forward+ Y + B) to deal massive damage to him. if he was still stunned after that quickly press RT for a buster move to deal even more damage. stage 100 is the easiest If you know the moves and how to avoid them.
For Vergil, If you don't know the Punch Line strat look it up on Youtube. basically, you just spam B and launch your arm to interrupt Vergil's moves. when your arm comes back to you after a few seconds, send it to him again. try not to attack him during his demon phase. wait until he does every move and turns to human. If he summons his shadow self, interrupt him with Punch line and use Devil Bringer to grab the shadow and use buster to finish him off (RT) in the air. If you manage to stagger Vergil, you have enough time to do Showdown and grab him with buster after.