This seemed like a pretty straightforward achievement at first, as you unlock cars progressively as you beat the game, but after I had beaten the game and conquered every race I realized I have only unlocked 30 cars.
You can unlock 10 extra cars by completing Reward Cards. You can check your progress in the main menu under the Reward Cards tab. The ones that unlock cars are marked with a car symbol.
EDIT: According to some comments, this achievement will unlock sometime while experience boosting online matches, so there's that for you ;)