I actually prefer this one over all the other Turtles games. Not sure why. It could be nostalgia, but I played Turtles 2 a lot more as a kid. I think it has more to do with it being more of a challenge, and I guess I also find beat'em ups a little bit monotone.
Why it has a shaky reputation? I think it boils down to the things said already in this thread.
It was too difficult for children at the time, therefore people remember it as frustrating. It also had a bit clunky controls. The jumping is a bit stiff. Some people also had problems with the swimming level. AVGN also pissed on it in an early video, which didn't help. However, a lot of people like it too, it was a superpopular game in its time... and I remember for a long time that was the video most people disagreed with AVGN on.
It actually had most characters from the cartoon. Bebop, Rocksteady, Shredder, footsoldiers, mousers, The Techmodrome, etc. Then all the Turtles, April, Splinter, the Turtlevan etc. Most of it is there.
It just lacked Krang and Baxter Stockman. This may have been due to it being more based on the original Mirage comics which didn't have these characters or the original TMNT movie. Krang first came later with the animated show. I think the problem is perhaps more that the developers chose to make a bunch new enemies along the stages so you wouldn't just be fighting footsoldiers.. which is fine, but many of them are so crazy and wacky in design they stand out too much.