Find a nice, long, straight stretch of road with a speed camera on it. Your best bet is the interstate/freeway. You'll need a fast car for this. Pretty much any exotic or supercar with higher acceleration & top speed. An easy car to do this in is the Bugatti Veyron because it has a very high top speed and acceleration. This can be made easier if you win events and earn upgrades for your car first. Equip anything that increases acceleration & top speed, including track tires, power shot nitrous, long gears, and aero body.
Floor the gas and hit the nitrous when you get close to the camera. If you trigger it while going at least 200MPH, you'll unlock the achievement.