Set up a freeburn and keep doing 1 race series. You should get it in no time.
You can start a race while in Freeburn by pressing start and selecting "Create Match" and setting up the points. Make them really close to each other for the races to pass very quickly. Once you select done, press left on the d-pad again and "Start" and do the race
source-
http://www.xbox360achievements.org/game/burnout-paradise/gui...