I have intentionally restarted 5 times on a few levels in an attempt to pop the achievement, but it hasn't done anything. I've tried doing it both by manually restarting and by putting myself in an unwinnable situation so that the game forces me to, and have completed the level after restarting many times in case that's a requirement, but I've still been unable to get the achievement to appear at all.

Given that no other Steam user has successfully earnt it I'm guessing that it's not just on my end.