To do this you will need to take part in Public Multiplayer races, and earn XP after each one.
You earn XP for doing various things, such as:
> Finishing a race.
> Finishing in the top half of the field.
> Winning a race.
> Finishing on the Podium.
> Having a penalty-free race.
You can also earn XP for completing various Milestones, such as:
> Reaching a certain number of races completed.
> Reaching a certain number of races won.
> Reaching a certain number of kilometers driven.
XP cannot be earned in the Online Championships or Custom Game portions of Multiplayer, which means there are no ways to shortcut this Achievement. You'll just have to grind it out and if you're fast/lucky enough you'll get more XP on average per race as the skill gaps between players seems quite high so far.