Why it was infuriating:
The game had some general weaknesses. The fun beat-'em-up platform was interrupted by annoying surface levels, and the ridiculously unequal weapon strengths made playing as anyone other than "I can kill from across the room" Donatello seem like a waste of time. You didn't get to choose, though, you just rotated through the Turtles as they died. All of this might have been overcome by the sheer Teenage Mutant Ninja Turtle-ness of it all, if not for one stage: The Dam.
The Dam level required you to try to beat the clock through a sprawling maze in order to defuse the bombs, which were prepared to unleash the fury of the Hudson River. See that pink seaweed shit? The stuff with an opening barely big enough for a mutated turtle to pass through? It killed you. It was ... electrified somehow. The science in the game wasn't all that accurate.
Setting aside the terrible example this set forth of telling kids the Hudson was safe to look at, let alone swim in, the failure to defuse the bombs resulted in an immediate game over, no matter how many Turtles were still alive. The margin for error was about one pixel wide and half a second long.
While it would be easy to pick on The Dam some more, we're going to have to go with the first time you make the mistake of running into one of the foot soldiers' rides while walking on the top level. You learn it doesn't just hurt you, it fucking flattens you.
Next Turtle, please.