This part of the other solution is correct:
Arcade is in Multiplayer mode. After you select it, choose the middle option for Official Campaign Tracks. Choose the first race for a short quick race.
However, the achievement does
not unlock right away. You need to
complete a track, and the game only counts it as complete once you've set a time and entered your name in the high scores.
The fastest way to do this is to complete the track once, and then pause and "give up." This will allow you to jump straight to the option of entering your name. Once you do so, achievement unlocked!