Go to "GRID Online", then "Events", then "Xbox LIVE" and select "Global Challenge". Here, you'll be able to select from 5 different events, where you can try to beat previously set targets, earning a bronze, silver or gold medal. Once you earn a medal, you will also earn some points towards the "Weekly Leaderboard" displayed in the main global challenge screen. The goal is to be ranked first, when timer in the top right hand corner expires. The timer should expire on Friday of every week. If you are having trouble getting first place, you can temporarily delete any friend from your friend's list until you unlock the achievement. If you are the only person on your leaderboard, you will still unlock the achievement, as long as you earned at least 1 bronze medal.
For the achievement to unlock, you will need to open up the global challenge menu after the timer expires. It will update you on your progress, and unlock the achievement.