Oh, so maybe you unlock the ability go to the menu. Because now I just press "O" and I'm there. Like, so easy I can't believe I couldn't do it before. So maybe it is unlocked.
So far I've beaten it with everyone except Mikey. I'll probably do that tonight. Raph is the only one at max level. So getting the others leved up will be my next goal after winning with Mikey.
Also, for anyone wondering, if you level up but go back to the map before finishing whatever level you're on, you do keep the level you gained.