TNT Racers

This is easily done in the normal challenges tutorial. What you need to do is to win a game of Knock-out mode, using pick-ups.
I found that I preferred driving ahead of all the cars and leaving them off-screen instead of knocking them out with pick-ups (the best one is the gun where you can shoot your opponent cars out with 3 bullets if they all hit the car).

Another good pick-up is the black shooter which slows down the other cars and makes them slide.

Once you complete the tutorial, the achievement will unlock.