As promised! Whole process took me about 2 hours.
I decided early on that I was going to do 4 Letter Word, Hopscotch, and Tunnel Blower first, since for me their kill boxes. Then it was Stag, Peel, Pepto and Lock Out. And then everything else in order. I ended up getting slaughtered on Hop Scotch and Tunnel Blower, but I finally got past them and basically speedran 7-4, 7-12,13,15...then died again on 7-17 due to a stupid mistake.
So I repeated the process a few more times, after dying even more, and finally
came to finish 7-19, where I thought the achievement would pop...it didn't. Turns out I forgot to remember to do 4 Letter Word first
, so guess what level I got to do last! Obviously I went very slowly, I even fucking walked the entire 7 floors of tiny saws, slowly jumping over each of them. And then, the achievement popped up, job well done!
But yeah, I've got to do A LOT of practice to do before attempting Impossible or Zombie.