Do the following achievements to enable the corresponding cheat:
April's adventure mode: complete the Ghetto level with Donatello
Casey Jones' adventure mode: complete the Subway level with Raphael
Shredder's adventure mode: complete Donatello's adventure mode
April's Apartment stage: complete the April's Apartment 2 level with Donatello
Autumn stage: complete The Dojo level with Michaelangelo
Foot Soldier's adventure mode: complete Raphael's adventure mode
HUN's adventure mode: complete Michaelangelo's adventure mode
Dojo Complete stage: complete the Turtle's Lair level with Casey Jones
Sewer Falls stage: complete the Sewer Falls level with Raphael
Sewers stage: complete the Sewers level with Leonardo
Splinter's adventure mode: complete Leonardo's adventure mode
Casey Jones' jacket costume: complete Casey Jones' adventure mode with April
Casey Jones' red shorts costume: complete the Ghetto level with Casey Jones
Shredder's gold costume: complete Shredder's adventure mode
Waterfall stage: complete the Turtle's Lair level with April
Shredder's Palace Exterior stage: complete The Lab 12 level with Leonardo
Subway stage: complete the Sparring With Splinter level with Leonardo