You need to complete a game of each game type. Fortunately, this is as easy as starting a game, right clicking, and then selecting "new deal" from the bottom. Then switch game types and repeat. As soon as you confirm the last "new deal," the achievement will pop.
Edit: You have to make one move (to start the game) in order to make it work. (Thanks, MichapX! I don't remember having to do this, but it might help and won't take any extra time.)