Bloody palace mode is unlocked after finishing the game on any difficulty. You will fight enemies on a floor and progress up the floor via portals. The fire portal takes you up 100 floors, the water portal takes you up 10 and gives you a white orb and the wind portal takes you up 1 floor and gives you a green orb.
You need to finish 9999 floors in one sitting to finish the mode. Every 10 portals you will face a random boss fight and bosses can be repeated on later floors as i faced jester and vergil 3 twice. After floor 9000 enemies will be in devil trigger and will have alot more health. To finish this mode quickly always take the fire portal unless your very low on health.
Enemy placements on floors are random and cannot be predicted but do get gradually more difficult on higher floors with chances or more enemies appearing being greater. Wrath is the only enemy i found that drops green and white orbs so if you need health may sure to collect orbs from these enemies. Near the exit portal in the lady boss fight wave i got there was a green and white orb i think this is the only boss that provides health when defeated. Also be warned that agni with both swords can also appear on regular floors but this only happed once for me on 6100.
I would advise waiting until you finish dante must die mode as you will recieve the super sparda costume (dante) which has unlimited devil trigger and health regeneration. You will also be able to use quicksilver and doubleganger styles with dante for an unlimited amount of time.
With this costume i equipped dante with rebellion, nevan, ebony and ivory, Kalina Ann and the quicksilver style.
With unlimited quicksilver i was able to easliy avoid enemy attack and kill enemies before any used healing or summoning abilities. This was very useful after floor 9000 as it allowed me to counter increased speed of enemies. I equipped nevan during boss fights to take advantage of air raid attack by flying and pressing x to take down bosses quickly and avoid alot of damage. This is most useful against vergil fights as you can easliy dodge most of his attacks while in the air.
This mode took me 2 hours and 30 minutes using super sparda and i barely lost 2 bars of health on any floor when using quicksilver.
Priorities enemies to take out summoning enemies first (Greed), then healing enemies (bishop) and then the most annoying that could cause most damage (Enigmas(shoot blue/red arrows) can be very deadly and hard to hit on higher floors)
If i have missed anything or there something i should add leave comments and ill try and make this more useful or reorder so it makes more sense. Good luck.