The Sun and Moon

System Two consists of levels 21 - 40 plus boss level II. These levels introduce you to more spikes and more involved phasing, as well as platforms that disappear and reappear. 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.

There isn't anything really complex in System Two, you'll just have to get used to curving inside walls and arcing in the air after launching. As for the boss level, this time he appears and disappears with the pink blocks, so make sure you time your jumps appropriately to get around him. 

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