To get this achievement, Levels 4 to 6 (Sector A-4 to A-6) must be completed. These levels can only be accessed after finishing the first 3 levels (Sector A-1 to A-3). Successfully completing Levels 4 to 6 will get you the achievement.
Here is a video by
Fire that shows the walkthrough for the whole game. The solutions for Levels 4 to 6 begin at the 0:50 mark and end at the 1:31 mark. Clicking on the video immediately begins at that point.
Specific points:
Level 4 - 0:50
Level 5 - 1:07
Level 6 - 1:18
Hope it helps.