Krang steals the Statue of Liberty, using his enlarged winged android body, before Shredder shows up on the television screen. In an attempt to stop Krang and Shredder, the Ninja Turtles battle their way across New York City. There, Shredder sends the Ninja Turtles through a warp across time and space.
There are some minor differences between the arcade version and the SNES game. For example, the SNES version level 4 is set in the Technodrome, from where Shredder sends the turtles on the timewarp. In the arcade game, he does it right after the Sewer Surfin' level.