This can be done with one controller being used, but you need to connect a second.
Go to Multiplayer then Splitscreen. You'll want to select Duel (2 players), Official Campaign Tracks and select any track (I used 1-1 for relative shortness and simplicity of the track layout), and once it's loaded hit X on both controllers.
You'll now have to race three times. You can ignore the second controller and use only the first controller to win; each race ends a couple seconds after you cross the line with the winning car.
The achievement pops after three races.