I actually thought this achievement was going to take a bit of time, but fear not! You do not need to select the "Racing" mode to get this achievement, you can also do this in the "High League" mode which saves you a lot of time.
The track in the Racing Mode will take you near enough 2 minutes a lap. If you select level 2 and put it on difficulty 1 (10 laps also if you wish) in the High League mode, this takes you about 20 seconds per lap.
The video guide shows you how to get 4 achievements including this one. Hope this helps!