Donatello falls asleep while playing video games, and dreams that he goes through several TMNT-ized classic games to rescue "princess" April. At the end of each level, he encounters one of his brothers, dressed up like the princess that fits that level's theme. After he rescues each, they say, "The princess you are looking for is in/on another dungeon/castle/space ship."
The first level is based on The Legend of Zelda. The boss for this stage is a Kraang, and the princess, based on Zelda, is Raphael.
Level 2 apes Super Mario Bros. and has Fishface as the boss. This Peach-like princess is Michelangelo.
The final level plays similar to classic TMNT games and has a distinct Star Wars homage atmosphere. The boss is a Darth Shredder and the princess is a Leonardo Leia. Outside of one of the windows, The Technodrome from the original cartoon series can be seen.