Here is the full list of all 23 TMNT achievements worth 1,000 gamerscore. It takes around 6-8 hours to unlock all of the achievements on Xbox 360.
Complete Level 1
Complete Level 2
Complete Level 3
Complete Level 4
Complete Level 5
Complete Level 6
Complete Level 7
Complete Level 8
Complete Level 9
Do a co-op move combination attack
Used Mikes special move
Used Leos special move
Used Dons special move
Complete a level without taking damage
Complete Level 10
Complete Level 11
Complete Level 12
Complete Level 13
Complete Level 14
Complete Level 15
Complete Level 16
Get your first coin
Used Raphs special move