Space A Go-Go
From the Super Mario Wiki, the Mario encyclopedia
The level starts at the bottom of the rocky mountain-island of High-High Island, and as Donkey Kong progresses through the level, he also scales to the very top of the island. Cranky Kong tells Donkey Kong that he will not be able to get King K. Rool unless he uses a Booster Barrel, and from there, the level takes place in space with Donkey Kong using the Booster Barrel to reach King K. Rool's ship in space.
There are also many obstacles in space, mainly meteorites, and as the level progresses, it becomes increasingly more difficult to dodge the meteorites. When Donkey Kong reaches the ship, he goes onto the next level.