Reposting myself from earlier in the thread:
There is a sort of news ticker at the bottom of the screen when you eneter the catfight arena. It will tell you about how good a day the contestants are having in vague terms, but it's not too hard to figure out which events would positively or negatively impact their morale or well-being. If most of them seem to be having a good day, exit the arena and re-enter it until the opposite is true for as many of them as possible. I'm not a 100% sure what those statuses do, but i assume they affect their chances of winning ties during matches. While you have to button mash really hard in those, it seemed to me like they are dependant on RNG. I found that i would win more ties when i was up against a fighter with a negative status message, while my own seemed hyped/fit. During the fights pay attention to what the strongest attacks of your opponent are, those are the ones they will likely use morst often. The majority of fighters have 2 attacks they're good at, with one being noticeably weaker. My strategy was to concentrate on those two and disregard the weakest one, even though it can come up occasionally. For example, if a fighter is good at paper and rock, i would keep using paper. If she chose rock, i would automatically win that clash, and if she chose paper, i would button mash to beat the tie and pray that the RNG is with me. If you're feeling confident you can also try to predict which attack she will use next, but that carries a bigger risk of you losing the clash. As for fighters you should bet on, the blonde teacher (Jennifer, Jessica?) has the best stats and i've had really good results with her, as long as i took her and the other contestants' status messages into account. Considering all of this, i've had a 50% winning ratio at worst and got the catfight related trophy (wins the tourmnament 10 times) in a couple of afternoons, while doing other side activities to break up the tedium and rest my hands from all the button mashing.