Instructions
Reach "The World that Never Was." This will happen toward the end of the game, after you have passed the "Space Paranoids" section.
Find Xigbar and defeat him. The best way to do this is to focus on your defense, and use Donald's comet attack as much as possible.
Go to Naught's Sky-way after the battle with Xigbar, and enter the "Hall of Empty Memories."
Go to the upper level of the "Hall of Empty Memories" and a cut-scene will begin. After the cut-scene, you will receive the Oblivion keyblade.