To compete in a PVP event, simply go to the Career tab from the Main Menu and select the PVP Events tab. Then you can select the Championship Playlist tab and select either:
-Rallycross Classic
-Rallycross 1600s
-Rallycross Supercars
Once you select one you will be put into a lobby to race in the vehicles of your chosen class. Once the race has finished, regardless if you win or lose, you get your achievement.