To get this achievement, you have to beat Fugue, the third level. There are 8 stages total, 4 on Side A and 4 on Side B. When you pass through green doors, it's the equivalent of a checkpoint, which is at each new stage. I've listed the name of each level below:
Fire in the Hole
No Man's Land
If you die, it will show you a map of the stage. The overall map stays relatively the same, but some small things may change in the layout of pillars and such. Try to map out the path you want to go after you've died to finish the level. It should be noted that dying doesn't affect this achievement.