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.
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....
Once again, these are mostly pretty easy. The only levels I see as bothersome are 2-4X and 2-8X.
Pay attention to his run of 3-11X at 3:23.
These levels are a lot more difficult than Worlds 1-3.
6-1X isn't that bad; it's easier than everything in Worlds 4 and 5.
I find 7-3X, 7-5X, and 7-15X to be not so bad.