The enemy in this game has a unique move that pushes back the party. For this fight only your party can do the same.
Whenever you inflict a certain amount of damage, the monster falls over. If you inflict a further set amount of damage before it gets back up, you will push it back. Repeat until he falls off the cliff. You may need to heal him in order to keep him alive long enough to do this.
Anyhoo, here's how to do the fight:
Try to get Firestrike weapons for Tidus and Auron. You can kill bombs and hope they drop firestrike weapons.
Start off by inflicting slow on the enemy, using Tidus' Stunning Steel (buy from O'aka) or the Slow spell. Use Auron's Power Break to reduce damage, preferably with a Firestrike weapon. Spam Fire with Lulu. Use Tidus' Haste on all three. Change Tidus' weapon to Firestrike, and spam Delay Attack.
At the start of the fight, you will probably get pushed back once, but when you are all hasted, you should be able to hit him quickly enough to push him back, and eventually off the cliff.
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