Start up any puzzle on hard and then hit the "H" key on your keyboard. Now click on either of the glowing tiles and they will be cleared off the board.
Repeat this until the puzzle is completed. If you run out of moves you can either load up a new puzzle or keep playing and either undo some of your moves or reshuffle the board, or both. If you choose to undo or shuffle it will not count towards this achievement, but it will count towards some of the other ones, like matching 10,000 tiles.
Once you complete the 10th puzzle on hard this will unlock.