Here is the full list of all 20 Drive!Drive!Drive! achievements.
You drove around a loop the loop.
You managed to turn your car upside down, many congratulations.
You drifted more than 200m.
You jumped more than 100m.
You smashed into an opponent in mid-air.
You smashed into an opponent from another track.
You obtained a medal of the golden variety.
You came 1st in all tracks in a race.
You made contact with a wall. Well done.
Yalopolooza! You smashed an opponent up.
You were taken for a ride. This time by a car rather than another human being.
You drove around a corkscrew.
You smashed into one of your own cars. From another track, obviously.
You smashed into an opponent from another track in mid-air.
You smashed into one of your own cars from another track whilst in the air.
You gave an opponent a piggy back.
You completed Campaign mode!
You completed Offensive mode! That's pretty hardcore of you.
You jumped more than 300m.
You drifted more than 400m.