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I think I defeated Emerald but not Ruby. For Emerald you needed the Underwater Materia. You also had to breed a Gold Chocobo so you could get the Knights of the Rounds summon on the little island that wasn't on the map. You also needed the Mime Materia, and the Materia that made you do your summon twice. So your character would do the Knights summon twice, then your other characters would mime it, dealing great damage. I don't think this was enough though. You needed the Pheonix summon joined with the Last Attack Materia, so that when you died you'd bring yourself back to life. I also used lucky 7 fever. Get all your characters on 7777 hp, and at the start of the battle, they'd automatically attack Emerald dealing 7777 damage each time, hitting it 50 times or something.