Final Fantasy IV/Bahamut

Fly to the Lair of the Father
You can only attempt to get Bahamut if you have already defeated Leviathan in the Feymarch. If you have done this you may continue. The moon is not a large area so it should not be too difficult to find the Cave of Bahamut. There is a circular plateau surrounded by another circular plateau. You must land on the outside circle with the ship, and then walk inside to the cave. Enter the cave.

Traverse the Cave
In the first room, go down and take the first right you can. Continue down and to the right, following the path until you reach the next room. In the next room follow the path again, going to the left, up and to the right until you reach a thin path. When you reach this path, you will be forced into battle.

Behemoth
These monsters are probably the toughest non-boss enemies you have faced so far. The key part about them is that for every attack you make on the behemoth, it will retalliate. So attacking with Rydia or Rosa's weapon would be foolish, as his attacks are quite strong. You will be able to continue through the cave once you defeat him. If you are struggling with these enemies, it would be best to leave the cave, and rest/save your game, as you will not need to defeat these again once you have done it once. If you can, use blink on all your characters, for once you do his attacks will usually miss.

Onward through the cave
Go up from where you fought the behemoth to the next door. On the other side of this door, go down the path in front of you. Along this path you will run into 2 more behemoths before reaching Bahamut. Defeat them, exiting and saving when necessary.

Bahamut
Defeating Bahamut is much simpler than it seems. He does not attack your party except for 1 devastating MegaNuke attack. He counts down as you are fighting, and when he reaches 0, he will unleash this attack, most likely destroying your whole party. However, by using Rosa to cast the Wall spell on several of your members, you will easily defeat him, as the spell will be redirected back onto him.. Use this technique while attacking with other members, and you will defeat him quickly. Once defeated, Rydia will be able to use the powerful Bahamut call spell.