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Monster Racers, perhaps? It's a DS title that, as its name implies, uses races rather than battles for its gameplay. In it, you compete against up to three opponents in 2D sidescrolling levels, dodging obstacles and hitting enemies. It has a decently-sized bestiary (you can recruit them all), the ability to breed any two breedable monsters to pass down a mix of traits and "IVs" (guaranteed to be the highest from each parent!), and has its own "legendaries" and post-game Battle Tower-like facility.
Extra note on the breeding: because you can breed down traits from any breedable monster family down to another, the only thing stopping you from using your favourites in your team is if they have a severely lacking base stat total.
