Must complete all events. Sprints, circuits, escapes, outruns, cost to states, cop takedowns, highway battles.
I prefer to use the Pagani Zonda. It goes very fast and has the best handling in the game. Handling really matters in this game. The Bugatti is the fastest car in the game but has really shitty handling. The Porsche Carrera GT and Lamborghini Murcielago are both pretty good cars too.
Remember, speedbreaker and NOS are your friends.
Dont worry about the other single player achievements, you will more likely than not get all of those while going for this one.