The Kupo Nut side quest involves traveling back to Gizamaluke’s Grotto at various points of the game to give a Kupo Nut that you receive to Moguta. You will automatically receive and give your first Kupo Nut to Moguta during a regular play through to help him escape from underneath the bell. Moguta and his wife can be found in the room at any point during the game.
You can only ever hold on to one Kupo Nut at a time and you will receive a new Kupo Nut at various points of the game after speaking to a moogle as long as you do not currently have one in your possession.
The first time you deliver a Kupo Nut to Moguta on any of the discs you will receive one of the prizes listed below. After you receive the prize below, delivering another Kupo Nut will reward you with a random item which will either be a Tent, Phoenix Pinion or an Ether.
The items that you can receive include:
Disc 1 - Holy Bell
Disc 2 - Elixir
Disc 3 - Extension
Disc 4 - Aloha T-Shirt
It is recommended that you try to deliver at least one Kupo Nut on each disc to obtain the items listed above, but the other rewards (Tents, Phoenix Pinions and Ethers) are not worth going out of your way to get.