I will get there one day, I SWEAR IT!

I had an A+ on every completed level.  Honestly though, there were only a handful of levels I didn't get an A+ on my first time through.  By the time I beat the level, I knew it well enough to get the par time.

Did you need to get an A+ on every level for it? or just complete the level

Holy shit I did it.  I still have 4 Cotton Alley Dark World levels to complete (9, 15, 16, 19), but I just got the achievement.  I'm guessing it's thanks to -1 worlds, but I'll take it regardless.   303 levels beat, 747 on the overall leaderboards.
 
Total Deaths:   8873 
Total Progress:  101% 
Light World:  100% 
Dark World:  97% 
 
Normally I'm just a straight-up achievement whore and would stop here, but this is such a damn good game I may just try to finish out the rest of Cotton Alley Dark World and the -1 worlds.