There is no set way to beat it. but there are two main methods.
The first requires:
- A good character with a decent strategy,
- A good deal of patience, and
- A lot of luck.
...I passed it using Yoshi, and eventually getting a hold of a screw attack. Jump, jump, stomp. Death going up, death coming down.
From there, it was just hoping a bob-omb wouldn't spawn on top of me while screw-jumping during the last 15 seconds... AGAIN.
The other method is cowardice, going by the theory that the enemies won't become harder if you don't kill them. I don't know if it works.
Go Moon!