You could do a lot more with this time travel concept in a direct sequel. Imagine the Turtles fighting in the Stone Age, Ancient Egypt, Medieval Europe, the Roaring 20s, etc. There are so many possibilities.

Anyway, this is great. Combat is fast paced and exciting, especially the bosses. I've never watched the TV shows or movies, but it seems like the source material has been captured properly (from what I can tell anyway). Visuals are appealing and well-animated, plus there's a very good soundtrack to go with it all. As a bonus, you have a neat little time trial mode, where you fight a collection of separate encounters back-to-back. It's very satisfying to achieve sub-10 second rounds.

As for criticism, double tapping a directional button to dash feels quite inconsistent to activate. This is annoying when it becomes the main method required to beat a certain enemy (though tbf, you usually have another enemy that you can throw into them and defeat that way). Also, stage hazards on the pirate level feel a little cheap at times.

As an arcade port, this won't take up too much of your time. I think it's definitely worth checking out if you haven't played it.