The Shredder fight can be done with both players on the screen with ease. Only one turtle has to hit the real Shredder and both Shredders will go after the one turtle as long player two doesn’t do anything. Both turtles can’t deal double damage to Shredder like with other boss fights. So it’s very easy to finish with both turtles, especially with the JP version.

I think finishing with both turtles is the true meaning of “co-op”. You can also steal lives from the other player in case one runs out of lives. There are avenues for both players to remain in the entire run that it shouldn’t be hard to make it to the end with both of them. Just my thoughts.