The Long Gui. They become available after completing missions 56-62.
The biggest creature, however, would be the Fal'Cie Titan. He's not a fightable opponent, but he can be interacted with and gives the party colosseum-type missions. Titan is that big rock man that you first see when you reach Gran Pulse; he picks up the Long Gui with two fingers and drops it into his mouth. -- ∙ ∙ 23:31, April 1, 2013 (UTC)