Simply enter Quick Mode, select Split Screen, join with your 2nd controller and set up any race (must be at least 3 laps).
Now when the race starts (you don't need to win it), just drive and finish it with your main profile and let the 2nd controller stay still - you don't need to finish the race with your guest profile.
As soon as you finish the race with your main profile a timer will start with a 30 second countdown (so everyone else can finish the race). When that countdown reaches zero, the race is over and the achievement will pop on the loading screen.