This achievement isn't very clear, and if you are like me, you'll instantly go to the quick game section, do the first puzzle in the minimum number of moves and wonder why the achievement doesn't pop.
The solution is simple - you have to be doing the Quest Mode for the achievement to pop.
Work through the first 4 or so screens in quest mode, defeat the first boss and then complete the next challenge after that. Once that is done, the first puzzle challenge will unlock.
It is a simple challenge that can be done in 4 moves if memory serves. Once you do it, the achievement will pop.