It's possible to do this achievement in a few minutes, if you are able to play the Windows 8 version of Mahjong.
What you do, is you play any puzzle on Win 8 until you have the last pair left. DON'T finish the puzzle. Instead, press the back-arrow so that it reverts back to main menu. Now, choose the same puzzle on your phone, then choose to use the Cloud-save. Now the game loads with the 1 pair left from your Windows 8 game.
Finish the game on your phone. Then play the Win 8 version again, choose the same puzzle again, local save, you should be still in the same situation with 1 pair left. Now, don't finish the puzzle, press the back-arrow again to go back to main menu. Rinse and repeat, load it up on your phone and finish again. You are able to finish the puzzle in seconds like this and it counts for all the stats like finished puzzles and winning in a row.