2nd Car, To win it go to the marker point and complete the two challenges, both can be done on Easy.
For the Drag race use the nitro in the 2nd straight, as you accelerate from the corner you should be able to see the light of the Supra behind you to judge when you need to hit the Nitro, its about half way down the first leg of the dog leg after the U turn. (this may make a lot more sense in the game as you'll understand the circuit.
Note Cheevo does not pop till you both win the car AND return it to the garage.
While I don't think its possible on this achievement, due to where it is in the story line based on comments only win one car at a time and then return it to the garage for its achievement to pop, for some cars its possible to "win" two without returning to the garage, doing so can mean neither achievements pops and you need to do them again.
Whist annoying reports are that if you exit the game and return it resets so you can still get the achievements but will have to win them again.