I got this myself a week ago. Some tips I worked out:
-Use Leo. Raph is good for his special attack, but lacks the range needed on many enemies. Don is too slow, and Mike lacks effective crowd control. Use Leo's special to give yourself breathing room, then close in and finish off individual enemies.
-Sewer Surfing: Stay on the lowest section to avoid the mines. There's only one there. Also, make copious use of Leo's special to knock down enemies, otherwise they'll overwhelm you.
-Prehistoric level: Use the special (especially as Leo) to quickly knock the dragon riders down. Cement Man is incredibly easy if you follow a certain protocol: attack 2-3 times (two to be safe), then wait for him to submerge and start moving. Run away in a straight line until he stops. If he is lagging behind you, STOP and let him catch up. Otherwise, he may cut you off on corners.
-Pirate ship: Go slowly, focus on bowmen, chakram users, and stonemen first. Don't fear the planks! They do damage, but if you're careful, enemies won't be able to inflict much damage themselves. If the plans are your main source of damage, you're doing well and can probably win.
-Tokka and Razzar was the biggest challenge, boss-wise. I know people say they're easy, to just jump-kick or attack + special to knock down, but it's never that easy, and the level is good at draining most of your health by the time you reach the end. I ended up using attack + special on the turtle, then jump kicked to finish off the wolf.
-Don't miss a pizza on Neon Night-Riders or you're screwed. Super Krang is INCREDIBLY easy. Attack from above or below, or at an angle. NEVER be in front of him to the left or right. Attack 3-4 times, back off to evade his counter, and repeat. Dying on him is unacceptable.
-Starbase: Go SLOW! Take your time, use Leo's special on the little robots, and stay on the bottom rank when handling the turrets and the rolling balls - this will keep you safe. At the ice trap, advance as far as you can before entering the trap, then kill everything. Now, wait for a chance and dash through quickly.
Krang: Leo's special attack makes quick work of Krang. Just stay away from his sides. Special from above and below Krang to pile on damage and kill the robots he deploys.
Shredder: This youtube video is the key:
While he doesn't follow it in the video, read the description for his strategy. Here it is:
#1 - Circle Shredder until he fires an energy blast from his hands. Then hit him a couple of times then back away. Continue circling and attack when he does this move again.
#2 - Repeat step #1 until Shredder uses his one hit kill move where he levitates
#3 - Once Shredder starts levitating, get above or below him. When he lands immediately hit him a few times then continue to circle him until he does that move again.
#4 - Repeat step #4 until Shredder dies.
Following this strategy is foolproof. It is perfectly safe to lay into Shredder after he uses the energy blast. He will jump back before he counters most times. The instakill move is an utter joke so long as you pay attention. He only uses these moves (and are his only ranged moves) when you are to his direct left or right, so you can completely control when he uses them.
All in all, I'd say my biggest challenge was Tokka and Razzar, honestly. Sewer Surfin' is annoying, but early enough it's not too bad. Starbase can be difficult, but take it slow and it's quite easy.