All you have to do here is finish all the Challenge maps. They're located at the NYC Map under Challenge Mode. The only one not required is the very top option, "Survival".
There are 4 rounds for each level:
I used Donatello due to his ability to gain back 20 health from knocking down 5 enemies in a row with the "Line 'em Up" upgrade under COMBAT. The level 3 move with the Gravity Gauntlet works very well for this. I also suggest unlocking the Unlimited Special Attack. With this you can build a 20 hit combo, roll out of the way, taunt and power yourself up with a 20 second unlimited special attack. Have the Gravity Gauntlets equipped and go to town with the level 3 attack (
full clockwise rotation).
If you prefer to use a different turtle that's fine. The most important thing is that you are proficient with their fighting style and that they're leveled up most of the way.