There's a trick to it! Thankfully someone reminded me of this because I had completely forgot about this trick.
Luckily, the Tonberry King skips his first 3 turns so you can get at least 2 moves in from each character before he starts attacking.
Your characters and soul breaks will differ from mine, but the basics are the same. Just get a couple moves in like Lifesiphon, Wrath, or basic attack if you have to, then flee. Restart the battle and rinse and repeat until everyone has as many soul break guages as you need. I had to use Entrust on poor Vivi and Edge since they don't have a means of building their guage quickly.
Then I just went to town.

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