Difficulty settings:
Easy:
Human
Normal:
Devil Hunter
Hard:
Nephilim
After completing one of them, it unlocks the next, then the next one, until the final difficulty setting:
Very hard:
Son of Sparda - Enemies get tougher, attack waves are remixed.
Harder than very hard:
Dante Must Die - Contains the strongest enemies and insane attack waves
Not that hard:
Heaven or Hell - The remixed mode, but everyone and everything, including Dante, dies after one hit.
Crap your pants hard:
Hell or Hell - The same as above, but only Dante dies after one hit.
I really hope we don't have to complete Hell or Hell to unlock the Platinum trophy. Such an unfair difficulty.
http://www.gamesradar.com/dmc-devil-may-cry-four-extreme-difficulty-settings-confirmed-unlockable/