The title refers to the original NES TMNT, not the arcade version or the NES game based on it. This is the version that Konami released under their Ultra label. It sold well (real well!) but is widely considered an inferior game for a number of reasons. Those reasons are the subject of these three videos, from Youtube channel Displaced Gamers. I recommend them, even if I think every place they say gamer it would be more proper to say player.
The first video:
In a long and difficult game, one of the hardest sections comes relatively early. The only swimming section in the entire game, players must maneuver their supposedly-aquatic surrogates through a difficult course that has imprecise movement, water currents, high damage, instant kill hazards, a strict time limit, and, as the video shows, buggy implementation. Many players in the NES era gave up at this point, which is rather a shame considering it’s only at the end of level two. This video examines the code and demonstrates why it’s so challenging, and how it could be made fairer.
The second video:
TMNT has notoriously floaty jumps, a low frame rate, and a fairly weird implementation of gravity. Any platform game that allows players to adjust their jump height according to how long the hold down the jump button is fudging its physics behind the scenes, but TMNT does it rather poorly.
The third video:
Displaced Gamers examines additional problems with the game’s timing, particular with that of its input reading and attack animation. Like the other two videos, they suggest code changes (sometimes in the form of Game Genie codes) that fix the problem, if you happen to have a fondness for 6502 assembly. (I do!)
If you’d like to try NES Teenage Mutant Turtles, it’s included in the “Cowabunga Collection” that was released for Switch, Xbox X/S and Playstations 4 and 5. Fortunately, it also includes twelve much more playable titles.