I generally rotate my fighting elements among those that are strong against that particular opponent. However, if I have multiple rounds where no element seems to work, I will start using the common single-element animal over and over.
I have also had a disproportionate number of times where I will battle for hours in an evening, go to sleep, and win the first round the next morning. It's as if the game takes pity on me. LOL
It does seem as if the probability of a win with a certain element is increased or decreased on certain levels in a tournament. Unfortunately, there's not really a way to know that until you've lost multiple times with that element.