You can complete the Chocobo Dive Spots side quest 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.
You can find the Treasure Chests in the locations listed below.
Mountain Crack #1
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.
Mountain Crack #2
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.
Achievement/Trophy
Obtaining the Genji Helmet is one of the requirements for obtaining the 
Path of the Samurai Achievement/Trophy.
Mountain Crack #3
The third crack is located just south of the second one on the Forgotten Continent. The rewards include a 
Maiden Prayer, a 
Dragon’s Hair, a pair of 
Gauntlets, and an Odin Card.
Mountain Crack #4
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.
