I love this idea of a thread.
My general definition of a catch level is when one can reach the finish with the time stopped since the first (or only) Time Travel, so the extent of getting the best time essentially ends long before actually reaching the finish.
That, however, does not intend to diminish the handful of levels out there where keeping the time stopped from the first Time Travel is difficult and requires either or both a lot of skill and exciting gameplay - Speed Attack is the first example that comes to mind.
I just rewatched the run of Bouncing Fun from the fourth rampage; I wouldn't consider it to be a catch level, as the time restarts thrice between the first time travel and the finish. The fact that time is stopped for the majority of the run, I think is countered by Xedron's blistering pace throughout the whole level and not keeping the time stopped from the beginning.
Despite this, mentioning Bouncing Fun did spark the thought that sometimes the definition of a catch level can be a case-by-case basis, and that a run in this category can be judged on its level of entertainment from a viewing perspective, and its level of entertainment from a room-for-improvement speedrunning perspective.
These are just some mildly scattered thoughts, but I hope it's a good way to continue. (I also finished writing this before I saw Mazik's post.)