There are three unlockable costumes in DMC: Devil May Cry on the PS3 and Xbox 360.
Here are the costumes you can unlock in the game, and how to unlock them.
Coatless Dante Costume – Complete the single player story on the Son of Sparda difficulty
Super Dante Costume – Complete the single player story on the Dante Must Die! difficulty
White Haired Dante Costume – Complete the single player story on any difficulty
The Super Dante Costume allows your Devil Trigger to not deplete over time, instead your Devil Trigger is only used when using abilities that require it.
Check out my other article if you need to know how to unlock the different difficulties in the game.