Simply by defeating all monsters in all 50 floors. No time limit. No restrictions or conditions. Just fight, fight(use a potion if you want) and fight some more. It's easier on Wii (in my opinion) than on Gamecube so all gamecubers watch your step carefully. Use a variety of techniques and make sure that you have finished the "City in the sky" before attempting to defeat the Cave of Ordeals because you neeed all dungeon items to go through the 50 floors.
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The cave of ordeals is a side quest. Every certain amount of levels you will encounter a faerie who will stock the light guardians ponds with faeries. Then at the bottom a faerie will give you a vial of faerie tears which will fill your life completely full and increase your power.
It is after you beat the Elite Four and become the champion. After when you go to meet the rockets they will have made a cave, then when you talk to them they will battle you. After you beat them, you can then enter the cave.
i can beat the first part of it.
It is Altering Cave which you can enter only after you beat the Pokemon league.
If you tell me where cappy is in the caverns, ill tell you how to beat it.