The underwater room of the Place of Memories (the final dungeon) contains a small alcove on the right side of the screen; Zidane will be hidden from view when you're inside it. Search the lower-left corner of this alcove with the action button until a menu pops up. Choose the second option to fight Hades.

Zidane and the Lord of the Underworld

   Did you really think FF IX wouldn't have a boss that counts down to a powerful attack? Hades does just that; he counts down from 3 to 0 and then casts either Curse or Die Hard. The former inflicts various status ailments on the team, so be sure to equip a lot of status-protection abilities before the fight. As you might expect, Hades is weak against Holy attacks. Since he casts Reflect on himself, you can't use the actual Holy spell (unless you debilitate him with Dispel first), so use Eiko's Maduin summon intsead. You can also steal a valuable Robe of Lords from him. Hades has about 50,000 HP. When he's defeated, he'll simply disappear; you'll get over 16,000 experience and 30 AP for the kill.

   From now on, when you search Hades' hidden lair, he'll let you into his hidden item-combination shop, which holds a number of exclusive items. By combining the two halves of the Ephemeral Stone, you can obtain Garnet's ultimate summon spell, Ark. Mixing the Tonbachi (obtained in the Zodiac Coins quest) and a healing stone gives you the very powerful Brick Armor for Steiner. Finally, if you've already learned Odin from the Dark Matter, you can combine it with one of the bracelets (the one with Phoenix Charm) to make a Protect Bracelet, though this item can also be found from Chocographs. Other rare items you can create in Hades' shop include the Robe of Lords (you'll have to give up both the White and Black Robes to do so), Ethers, Phoenix Pinions, and Beatrix's Save The Queen sword (you can't equip it, but Salamander can throw it).