Obviously, you're going to need the Cops And Robbers
DLC to get this achievement.
Then, you'll need at least one more person to play against online (a boosting buddy will make it much easier). Choose Cops and Robbers from the options and make sure you're a robber for this achievement.
When the game starts, move toward the 'Gold' by following the beacon and once you've picked it up, return it to your 'Base'. If you're lucky enough to be boosting, just have your buddy sit there and do nothing. If not, you must have more score than the cops when the timer runs out.
If you manage to get the gold back to your base, you'll also nab this achievement: -
The Golden achievement in Burnout Paradise worth 71 pointsAwarded for delivering the Gold to your team base in a Cops and Robbers game on Xbox LIVE
Now just do the reverse to win with the cops and get this achievement too: -