When Raph tells Donny his mutagen tracker is as useless as a trench coat on a turtle this is possibly a reference to the original Teenage Mutant Ninja Turtles (1987) series where the Turtles would often go out in public wearing masks and trench coats. It could also be a nod to the Teenage Mutant Ninja Turtles (1990) movie where Raphael went out in public at night wearing a trench coat.
When Miley finds the second container of mutagen he says "go ninja go ninja go" this line of dialogue is the chorus of Vanilla Ice's 'Ninja Rap' from the movie Teenage Mutant Ninja Turtles II: The Secret of the Ooze (1991).
The Turtles take on Karai and her robotic Foot Soldiers. This is a nod to the 1987 animated TV series, where all Foot Soldiers were robots.