Alright, this is a solution that will allow you to win every race in your first try!
The objective of this achievement is to place third in every exhibition race. There are 15 or 16 races. Your objective is to place third, not to get the fastest time in the game. This isn't Time Trials.
So with that being said, go to your career, and buy a car menu. Select an Acura RL A-Spec. This is a D 399 class car. Now go to Upgrade and select:
1. Anti-Roll Bar: Progress-Sport Anti-Roll Bar
2. Transmission: Comptech Street Transmission
3. Clutch: Street Clutch
You should be at a D 400 class now.
Now in all of the races, the computer cannot select AI opponents above your class. Do if you have a D class, the AI cannot be C class or higher. If you upgrade your Acura as I have said, you should have the most powerful engine in the D class, at around 300hp, and great handling. Although when you look at the stats, and it says you a 3.1 on acceleration, it is inaccurate. You Acura will out-accelerate any other D class car, the computer puts you against.
I won every race by margins of 6 sec. or better. You don't have to be the best driver, I went off the roads many times and still came back to win the race, do to the speed of the car.
To unlock the achievement, simply place third in every race. Remember that the objective is to be in third place, not the fastest car in the game. Your car will have a max speed on flat land of around 115mph. That makes your car a lot easier to handle then a car going 200+mph! The Bronze, Silver, and Gold achievements are stackable. So If you unlock either Silver or Gold, the Bronze will subsequently unlock.