You only need to complete 200 games, win or lose. After earning the 15,000 points required for the "Emperor of Carcassonne" achievement, you will still need to complete over 100 games. The fastest way to do this is in local multiplayer. See "Count of Carcassonne" for more information on setting this up. Each game you just jam all tiles down with both of your players as fast as possible. Doing this, you can complete each full game in around eight minutes. To boost the last 100+ games, this will take you another 15+ hours. Be sure to turn off the River II expansion as it just adds more tiles to the mix, increasing each game's length.
You can check your progress towards this achievement by clicking on "Profiles" from the Main Menu and selecting your gamer profile.