Okay, so far I've only managed to beat Big Bang Coliseum and I have to say...I'm not getting it. The Centaur talks about "the legendary breeder" and breaks the star rock into 12(?) pieces and does something with them. (the latter of which hints to a sequel) but the part I'm confused about is the legendary breeder. The "the" in that title makes me think that he's not just calling me legendary because I'm awesome.

The one thing I did notice was that the game vaguely hints towards Electra being Cleo's mother...but maybe I'm just making assumptions.

Perhaps if I played through the game again I could make more sense of it, but I don't want to lose my monsters.

You just aren't getting it.

The 12 pieces are the fragments held by the Zodiac Monsters.

There are still another big 4 tournaments plus the Legend Cup.

Electra is not Cleo' mother.