Broken Base: Which version is the better version: The NES or Arcade version? Heck, just comparing the music between the two versions (higher fidelity versus smoother instrumentation) can cause a fight.
Surprisingly Improved Sequel: The NES version, despite its previous game was a TMNT game In-Name-Only, had characters from the show, ranging from: Bebop and Rocksteady, Granitor, to General Tragg, had a very fluid battle system and set the stone for the next two TMNT console games.
Krang takes way more damage than anything before him and will hit you with a kick attack that does a lot of damage and has a lot of reach whenever you get near him, meaning about the only reliable way to hurt him is with jump attacks.
Shredder himself, despite already being the final boss. Between his duplicates making it almost impossible to tell which is the real Shredder, and his One-Hit KO attack (which if he and a clone use is guaranteed to kill you), the final battle can be downright infuriating. This is on top of him being fought immediately after the above mentioned Krang.