Of course there was that time I caught a Treequatro. You know, the ultra-rare Grass-type Legendary Bird that can only be caught by fishing off a specific spot on the coast of Cinnabar Island with six Missingnos in your party...
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Nominate Balthier/Dr. Cid for the Greatest Game Rivalry Contest
Also Tidus/Jecht, Squall/Seifer, Sora/Riku... but mostly Balthier/Dr. Cid :)