From the Super Mario Wiki
High-High Island is a very tall and desert-like island that appears in DK: Jungle Climber. After exploring Chill 'n' Char Island, King K. Rool with his King Kruiser IV is flying into space and the Kongs tried to find out a way to go after King K. Rool, then Diddy Kong notices a tall island that the King Kruiser IV is heading towards and the Kongs attempt to climb it. Though very tall, High-High Island only has two levels (excluding Little High-High Island). The Kongs also use the Booster Barrel here, and rematch Mega AMP on King Kruiser IV.