To combat Vanitas Feeling:
Finish the story and go to the save point in the Necropolis Keyblade . There, a kind of sign shining in a rock. Get close and accept the fight. Please note, you will need a very high level to successfully overcome Vanitas Feeling.
To face the Mysterious Fighter :
Remove Vanitas Sense and go to the land of Departure. You have to beat the mysterious figure with all three characters.
