I second Vodelle's comments.
I'm a newer player (level 23) and managed to win this tournament with relative ease using only a few level 15 Super Rares (and, of course, some luck).
I learned to pretty much stop feeding animals that are just 'Rare' or 'Common' and only feed the 'Super Rare' animals until they are the highest level (I'll work on the other animals after I run out of Super Rares to level). This way I have a variety of decent fighters for tournaments. I don't have any gem creatures or other special elements outside of fire, nature, earth, lightning, dark & valentine. I did get stuck on the Toucan in this tournament for a bit, but otherwise I finished it with a couple days to spare.