Chocobo's Air Garden

Location

Each time you load a saved game, the location of the Chocobo's Air Garden moves. Luckily, it's always in one of five places. To the right is a map showing all five of its potential positions, both where they appear on the world map and what the location actually looks like in the overworld. You'll know when you've found the right place because the Chocobo's Air Garden casts a circular shadow on the ground below it. While standing on this shadow, feed your gold chocobo a Dead Pepper and it will fly up into the Garden. After your first visit the Garden will be marked on your map so you no longer have to guess at which if the five positions it's occupying.

Ozma  

In the upper left corner of the Garden sits a pointy rock formation that Zidane calls an Eidolon Cave. The first time you examine it, Mene, the Moogle that runs the Chocobo Hot & Cold mini-game, will approach and tell you that a powerful force rests inside. Examine the cave a second time to start the battle.