If you think about it, Out of the Shadows was the closest to the 80s cartoon.
Ignoring the fact that it's a direct sequel to the 2014 Michael Bay produced movie, it felt like it hit all the right notes for being similar to the 80s show. I mean, it had Bebop and Rocksteady making their live action debut along with Baxter Stockman, and Krang is the main antagonist, complete with the Technodrome, his personal battleship, making an appearance and serving as the backdrop for the final fight with Krang. Also the Foot Clan felt more like ninjas instead of ripping off COBRA from G.I. Joe from the 2014 one. Oh, and it even uses the old theme music over the end credits.