The Deep Sea Deposit is the second half of the Deep Sea Research Center area. There isn't much to see here along the linear path other than a few Draw points. Your main goal is at the bottom, provided you have at least 10 RSP left from the Deep Sea Research Center.
Note that if Zell opened the door to the Deep Sea Deposit, you will be forced into a number of set battles. You cannot run from these battles. There are three per screen, and they grow increasingly difficult. You'll have to fight them again if you change screens, so once you start down the path, you'll want to keep going. There is a hidden save point at the bottom which you will definitely want to take advantage of after all those fights.
Once you reach the bottom and use your 10 RSP, Ultima Weapon will appear and attack. Don't forget to Draw Eden from this boss!
Note that if Zell opened the door to the Deep Sea Deposit, you will be forced into a number of set battles. You cannot run from these battles. There are three per screen, and they grow increasingly difficult. You'll have to fight them again if you change screens, so once you start down the path, you'll want to keep going. There is a hidden save point at the bottom which you will definitely want to take advantage of after all those fights.
Once you reach the bottom and use your 10 RSP, Ultima Weapon will appear and attack. Don't forget to Draw Eden from this boss!