NOTE! For this achievement, you must have Wing Boots, meaning you must be aware of this achievement before you enter part 2 of Round 7.
When you reach part 1 of Round 7, which is a town infested by blue and red rats, you go all the way to the right to talk to the guy in there. That activates a platform that leads to part 2, where you can obtain this acheivement.
With the platform activated, go back to one of the first shops in the town and pick up Wing Boots. Hit the Hospital if you have to, but do so before buying the Boots. With the Boots on, rush as fast as you can toward the platform that activated earlier and jump up to the clouds.
When on the clouds, rush to the right to get to the end where there's a cloud you cannot reach without Wing Boots. I managed to get all money bags on the way there, but that was lucky and is not something you should count on. Focus on hitting the right-most cloud while your Wing Boots are still active, since they only stay active for something like 30 seconds.