Final Fantasy IV/Giant of Babil

Enter the Giant
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.

Four Elements
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 elements once again. Use the same weaknesses from earlier in the game (Milon-fire, Cainazzo-Lit, Rubicant-Ice).

CPU
Once you have defeated the 4 elementals again, you can continue on to the next staircase. In that room is the CPU. There is a very specific way you must fight this enemy. First you must kill the small ball on the bottom. This is a defender who will otherwise heal the large CPU. Then you must NOT kill the other small orb, or the large CPU will attack you with a devastating spell. Once the defender and the large CPU is dead, you can kill the last one.

Because the CPU uses Wall and because you can't kill the Attacker orb, Rydia's best spell for this fight is the Sylph summon.

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. Finally Kain will get you out of the giant and rejoin your party. The ship will fly back to the moon.

Optional Sidequest
This would be a good point to attempt attaining both call spells Odin and Bahamut.