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You live in a world where all the animals look cute or weird and have special powers. You catch these animals and make them fight against other people's animals, to gain fame and become the champion of the sport.
They're also associated with various elements each, and depending on what elemental attack you use against an animal, it'll be more or less effective depending on its type. There's also attacks which make them fall asleep, weaken them, temporarily boost your own animal's abilities, and so on.
The battle system actually has a lot of depth to it, and you can breed animals for stats and rare attacks, carefully plan their movesets and training, and then test your skills against other players online.