To unlock a new costume, simply reach the required level on single-player mode. The first two costumes are already unlocked.

Costume	How to unlock
Cowboy	Reach level 23
Desert Camo	Reach level 07
Future Warrior	Reach level 38
Gold Uniform	Reach level 99
Ninja	Reach level 50
Panda Suit	Reach level 60
Policeman	Reach level 10
Sky Camo	Reach level 18
Tough Guy	Reach level 15
Urban Camo	Reach level 30
Virtua Cop	Reach level 34
World War II Uniform	Reach level 20