Here's how Bizarro works. His parts enable different attacks for him to use, but the Core is what lets him use Bizzaro Enegy (as it appears). Usually, you can smash through the torso and not bother with the parts but I set it to give Recovery instead so that his mechanics have to be engaged (unless you get a very lucky Omnislash + Highwind).
To make the Core vulnerable for Team A, you need to kill the Core segments with the other two teams. Start by destroying the Head or one of the Arms with Team A, and swap to another team (it seems to be random, unfortunately, but it cycles to an extent).
Team B and C in their battle need to kill the Head, then the Arm (which has two parts for Team B), and then the Core. If you kill the Arm without killing the Head, then it will revive the Arm and the Core Segment will remain invulnerable. Once you've killed the Head and Arm, you can destroy the Core Segment. Ignore the option to swap teams until you've destroyed that Core Segment, then swap teams.
Hopefully, you'll be put in control of your third team. If not, destroy the Head (which revives for that reason) or the other Arm and select yest to swap again. When you get your third team, do what you did before. Destroy the Head, the Arm, and then the Core Segment. After this, you want to return to Team A.
Team A can now destroy their Core. Kill any remaining Arms (take care of the Head too, I think it enables the core to use Stigma) and start battering the Core. When it dies, Bizarro loses his ability to use Enegy and heal himself. Now you're in the home straight, batter the torso until he dies. The Head will revive periodically to use Heartless Angel and/or Aurora Fence; kill it if you like, it reduces Safer's HP by 200 every time you do.
So it basically requires three parties that are reasonably well-equipped to win through. The idea was that the final bosses would be fought after the other content, so they're quite tough (though Safer may be easier because of his AI pattern and the fact that he's a single-target). Let me know if you encounter problems with the way the battle functions, though it's been tested by myself and I think a few other people have done it too.