Essentially this achievement is for beating the 3rd mirror stage, as you need to beat the first two and get those achievements before even getting to do the third one. Gotta love those beats~
This level is a bit of a toughie, but if you can do the 2nd level's boss without dying, then you're fine. I believe in you!
I made a video included showing the 3rd mirror level completion. Solutions to the other two levels are included on their respective achievements.