Chocobo Dive Spots
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 dig up and then use Dead Peppers in certain areas of the map identified by bubbles floating up to retrieve treasure chests.
The Treasure Chests can be found in the locations listed below.
Path of the Samurai
Dive Spot #4
The fourth Dive Spot is located on the east side of the Mist Continent but is much easier to obtain but going into Quan’s Dwelling as shown in the screenshot below. Attempting to dive on the actual spot will usually take multiple attempts, but if Choco dives down from atop Quan’s Dwelling there is a 100% chance of success. The rewards include 9 Ore, 15 Topaz, Tiger Racket and a Red Rose Card.
The Ultimate Racket
The final Dive Spot can only be reached on Disc 4. Travel back to where the Shimmering Island was located to find a new Dive Spot. There are no bubbles that appear to help you find it so you may have to use a couple of Dead Peppers trying to find it. Use the screenshot to help you identify the location. The rewards include 10 Aquamarines, Ultima Weapon, Maximillain and an Invincible Card.