Chocobo Mountain Cracks
The Chocobo Dive Spots side quest can be completed after you have obtained the Ocean Ability for your Chocobo by completing the Chocobo Hot & Cold side quest (check that page for more information). Once you have the ability, you can find cracks on the sides of mountains and then use Dead Peppers to retrieve treasure chests.
The Treasure Chests can be found in the locations listed below.
The first Mountain Crack can be reached once you get the Blue Narciss on Disc 3. Travel to the Outer Continent (northwestern continent covered in snow) and search the area in the northeast for a crack on the side of the mountain. Open it to receive 41 Lapis Lazuli, a Rosetta Ring, a Protect Ring and an Airship Card.
The second crack can be reached when you gain access to the Forgotten Continent. The spot is located in the middle of the continent just south of where the Hilda Garde III lands. The rewards include 19 Eye Drops, a Madain’s Ring, a Genji Helmet and the Hilda Garde I Card.
Path of the Samurai
The fourth and final crack is located on an island just north of the Outer Continent. It is used to gain access to Mognet Central which is part of the Mognet Central side quest.