The below videos have shown me how to do many levels I was stuck on in the process of attempting this achievement, as well as a few tricks that made some hard levels a joke. It's worth noting that he uses The Kid (unlocked by beating the Warp Zone in 5-7) in many levels, particularly in World 5. While unlocking The Kid is no joke, it makes beating the 85 levels you need to a much easier task. And while the other solution says to try and stick to worlds 1-4, I have found some levels in the later worlds that aren't too bad. ALL credit goes to DurrpyProductions on Youtube:
The Kid Warp Zone:
Level 1: There's really not too much advice I can give other than don't run up until the very last jump.
Level 2: For the set of spikes that are closer together, I found it a bit more efficient to run, but not weave completely to the left or right, just enough to avoid the spike.
World 1:
These levels are pretty straightforward. If you're having trouble on any of these, you should probably get a little better at the game in general before attempting Dark World levels....
World 2:
Once again, these are mostly pretty easy. The only levels I see as bothersome are 2-4X and 2-8X.
World 3:
Pay attention to his run of 3-11X at 3:23.
World 4:
These levels are a lot more difficult than Worlds 1-3.
World 5:
World 6:
6-1X isn't that bad; it's easier than everything in Worlds 4 and 5.
World 7:
I find 7-3X, 7-5X, and 7-15X to be not so bad.