The Sun and Moon

System Five consists of levels 71 - 90 plus boss level V. Remember that there is no time limit for completing levels for this achievement, so take your time so you don't die needlessly over and over.

System Five starts off innocently enough, with some platforming levels from 71-80. Then things get complicated, as you're first introduced to platforms that appear when you phase, and then also to platforms that disappear when you phase. It will definitely take some practice and dexterity to get used to these levels the first time you play them, since you'll constantly be under- or overshooting. Practice makes perfect with these levels, and you'll definitely need it, because the boss battle has a relatively fast boss chasing you while you have to make ground appear and phase in it throughout the entire level. This will again just take practice to get used to controlling yourself and moving around the level in a controlled manner. 

Upon completing all 20 levels and boss level V, the achievement will unlock.