The Sun and Moon

System Four consists of levels 61 - 70 plus boss level IV. 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 Four doesn't introduce any new concepts or anything, it just has more involved platforming or curving while phasing into structures. It's a welcome break after some of the System Three levels. The boss battle can be a little annoying. Every couple of seconds the boss will dash at you. Just be ready to jump or phase out of the way at a steady frequency the entire time. 

Upon completing all 10 levels and boss level IV, the achievement will unlock.