How to Complete It's a Secret to Everybody

This quest becomes available after you have completed Flown the Coop.

The objective is to weaken Titoise and defeat all foes. Titoise is one of the Great Tortoises, so defeat the Chocobos (or catch them with Chocobo Knights), then kill the Great Tortoises that aren't named Titoise, and finally weaken Titoise to HP Critical status. The Chocobos are weak to Air and they absorb Earth. The Chocobos are weak to Water, Holy, and Lightning.