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. Directly west of the Crystal Palace, 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.
This dungeon has a fight against 3 Behemoths and Bahamut, aim to have at least a full stack of Hi-Potions and Phoenix Downs, as well as grinding Lunar Virus, Eukaryote, Prokaryote, Black Flan, and Moonmaidens for as many Lunar Curtains as you feel comfortable. Reflect is essential for Bahamut.
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.
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 retaliate. So attacking with Rydia, or Fusoya's or Rosa's weapons would be foolish, as its attacks are quite strong.
The easiest way to beat these are to start off by having Edge use Mirage, and having Rosa and Fusoya apply Blink to the entire party. Once everyone is Blinked, unleash hell on it. Have Rosa use Berserk on Edge and Cecil, Fusoya use Holy, and Rydia use whatever -aga spell she can. At some point it might use Maelstrom, which is a party-wide version of Tornado, so just use Curaja from Rosa on the whole party if this happens. If someone dies, use Arise from Fusoya on them. Eventually it will die, and you can continue the dungeon.
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. Keep in mind that you only need to beat them once.
Defeating Bahamut is much simpler than it seems. He does not attack your party except for 1 devastating Mega Flare 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 Reflect 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 summon.