If you have a Windows 8 Mahjong alongside your phone, it's possible to get this achievement in a few minutes. First, play Windows 8 Dragon-puzzle until you have your last pair left. Then, DON'T finish the game, instead, press the back-arrow to revert back to main menu.
Now, play with your phone, choose the Dragon-puzzle, then use the Cloud-save. You should have the game where you need to connect the last pair. Do that, that's one game finished.
Now, load up Dragon again on Windows 8, and choose the local-save. Your last pair is again there. Press the back-arrow to revert back to main menu and rinse and repeat this with your phone until the achievement unlocks.