From Final Fantasy Wiki
Bahamut's Lair, also known as Cave of Bahamut, is an optional area in Final Fantasy III on the Floating Continent. The cave itself is located to the southeast of Vikings' Cove, but the player must cross the mountains to the east of Bahamut's Lair in the Invincible to reach the entrance. The party can fight Bahamut here in order to obtain him as a summon. The player must first travel through the cave and return to the entrance in order to fight Bahamut.
Treasure
Encounters
Battle Background

Music
Bahamut's Lair background music is Final Fantasy III's "Dungeon" theme.