This achievement will unlock after you have earned a 3-star rating on 40 different levels. Repeating levels does not increment the counter additional times.
To earn a 3-star rating on a level, you need to end the level with five or more lives. Most maps from 1-100 are reasonably easy to do this on. Note that you can purchase extra lives from the store as you earn money in the game, and doing so early on will make the 3-star ratings easier. On some harder levels (generally 101+) there are also extra life tokens that will restore a lost life. You lose a life if you collide with any other in-game object. Generally your phone will vibrate to tell you this, and your vehicle flashes and turns partially transparent for a few seconds as well.