tmnt (21 Q) does not show up on a search for 'teenage' while asking a question, nor is teenage-mutant-ninja-turtles a synonym or anything. If I hadn't clicked on a tmnt question, I would have no idea what tag to use when asking a Teenage Mutant Ninja Turtles question.
Unfortunately, it's too long.
teenage-mutant-ninja-turtles has 28 characters, which is 3 over the limit. You could try it without the dashes, but that makes for an ugly tag.
We can now rename it
All sites are now allowed to use tags with 35 characters. Thus we can rename this tag to teenage-mutant-ninja-turtles.
TMNT is the accepted abbreviation for the franchise, to the point that one of the movies was specifically titled TMNT. It's pretty clear what it means. Even a Google search for TMNT brings up "Teenage Mutant Ninja Turtles" first thing.
However, the other short name, ninja-turtles, would make a good synonym.