Each costume is only available for the challenge map in which it was unlocked. You must complete the bronze, silver and finally gold medals for each before you can use them on the Infinite mode of each map.

Deadpool's alternate costumes and challenges needed to complete:

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




Once you reach Gold it might get a little too tough for you. Just use the hammers and the Harrison Cls. Pulse Rifles (Cable's future guns) which will make short work of the baddies. Use your momentum combos whenever because you gain momentum pretty fast and can recover without too much trouble.
If you're still having trouble and it takes more than a couple tries to defeat the gold medal, upgrade the weapons you plan on using through the campaign as much as you can. There's so many enemies though that the upgrade for charging the pulse rifles will be useless since you'd just be wasting time charging them anyways.

Well hopefully this mini guide will help anyone out that was having trouble. Now go kick some ass!