Play as Vergil:
To use Vergil in Story mode, have a saved game from Devil May Cry 3: Dante's Awakening on your card, or beat the game under any difficulty.
Bloody Palace mode:
Have a saved game from Devil May Cry 3: Dante's Awakening on your card, or beat the game under any difficulty.
Very hard difficulty:
Fail a mission under hard difficulty.
Dante must Die difficulty:
Beat Hard difficulty.
Super Dante:
Beat the game under Dante Must Die difficulty to unlock Super Dante. He's got unlimited Devil Trigger.
Super Vergil:
Beat the game under Bloody Palace mode to unlock Super Vergil. He's got unlimited Devil Trigger, too.
Alternate ending:
Kill at least 100 enemies during the ending credits.