Final Fantasy IV/Giant of Babil

Enter the Giant of Babil
As you arrive back at Earth, you will land automatically and all of your friends will arrive to stop the giant in its tracks. This will allow you to get inside the giant. When you regain control of your party, you are inside of the giant.

Inside the Giant
First head straight ahead and into the staircase, then through the next staircase. In the next large room, follow the path around, until you reach a point where the path forks. Go up and to the left and you will find the next staircase.

Stomach
In the stomach, there are three paths ahead of you. Go to the middle path (head to the right, then the first path you reach). Head around the room until you reach the next staircase.

Boss: Four Elemental Archfiends
In the passage, simply follow the path, use the save point you come to, then go on ahead to the next staircase. Inside the lung, walk forward, and you will be drawn into battle with the 4 elemental archfiends once again. The strategy is mostly the same as dealing with them before, except that they don't change forms.

Scarmiglione
Fusoya and Rydia: Firaga Rosa: Heal, Berserk/Haste Edge: Flame Cecil: Attack

Rubicante
Fusoya and Rydia: Blizzaga Rosa: Heal, Berserk/Haste Edge: Flood Cecil: Attack

Cagnazzo
Wall of water is always up, thunder does not remove it. Fusoya and Rydia: Thundaga Rosa: Heal, Berserk Edge: Blitz Cecil: Attack

If your mages are running low on MP, take this time to use Ethers.

Barbariccia
Can cast Maelstrom, a party-wide Tornado. Rydia: Any -aga, or Bahamut Rosa and Fusoya: Heal every turn Edge: Attack Cecil: Attack

Before proceeding, unequip all gear from Fusoya, because he will be leaving your party after the next fight.

Once you have defeated the 4 elementals again, you can continue on to the next staircase. In that room is the CPU.

Boss: CPU
There is a very specific way you must fight this enemy. First you must kill the small ball on the bottom. This is the Defense Node, who will otherwise heal the large CPU. Then you must NOT kill the other small orb until the very end, or else the large CPU will attack you with a devastating spell called Object 199 which hits for 9999 damage on several party members.

Because the CPU uses Reflect and you can't immediately kill the Attack Node, Rydia's spells are all useless, aside from the Sylph summon. Have Fusoya and Rosa cast Haste on Edge and Cecil, and then just keep the party healed as they pound away on the CPU. You can use a lower level heal like Cura or Curaga to save on MP, since Sylph's Whisperwind will also heal you for around 300-500 HP.

Kain
After defeating the CPU, Golbez will appear in time for Fusoya to bring him back to normal. He will reveal that Zemus is responsible for controlling him and that he's Cecil's brother. Finally Kain will get you out of the giant and rejoin your party. The ship will fly back to the moon.

Optional Sidequest
If you have not already done so, now would be a good point to attempt attaining both summon spells Odin and Bahamut. You must have defeated both Leviathan and Asura in order to get them. Additionally, you have a couple new items to grab.

The GBA and PSP versions of the game will also have the Cave of Trials unlocked now, as well as the ability to swap party members.

Kokkol's Forge
After obtaining Excalibur, Kokkol has some items for you to purchase now that you've defeated the Giant.

Sylph Cave
Make your way back to the Sylph's Home, and examine the bookshelf to the right of where Yang was sleeping.