I just got this achievement so I figured I'd throw my two cents in for anyone having trouble. I'd already tried several times with Raphael and Leonardo with no luck. On my best runs I was able to get to Starbase, but I'd die before I could even get to Krang. On a whim I decided to try using Donatello (he's my favorite character). I got the achievement on my first try with him.
I'm just saying don't automatically rule him out. Sure he's the slowest, but he has the highest defense and his range is good for hitting multiple guys at once. Plus, I'd say his special is just as good as Leo's (maybe it doesn't cover as much area, but it definitely covers more distance).