This can be done in the free version!
From the Main Menu, select the Matchup tab. If you have not bought DLC for the game, you'll only be able to participate in Sorcerer's Lair matchups. Choose Sorcerer's Lair to continue.
It will select three opponents and rank their difficulty based on score. Obviously if you want to get this out of the way quickly, chose the green difficulty. All you need to do is beat their score in the game. There isn't some weird multiplayer mode, it's just your score versus theirs. The green opponents have very attainable scores; I beat my opponent by a few million points in my first game.
Once you have beat them and the match concludes, achievement unlocked!