Earn a "Gold" medal in the indicated Challenge map to unlock the corresponding costume, as well as Infinite mode for that particular map.

Costume	How to unlock
Ballerina Deadpool	Great White News HQ.
Chef Deadpool	Citadel Courtyard.
Classic Deadpool	The Watching Sentinel.
Classic X-Men Deadpool	Beneath the Streets.
D-Pooly Deadpool	GRT Plaza.
French Maid Deadpool	Magneto's Prison.
Ultimate Deadpool	Catacombs of Genosha.
Uncanny X-Force Deadpool	Inside the Tower.
X-Men Deadpool	Office Spaces.