Reach Online Fame Level 30.
You gain Fame Points (FP, the equivalent of career-mode XP) by entering tournaments and competing in online races. Thankfully, level 30 is not too much of a grind and is pale in comparison to what some other racers have (level 280+). However it’s a bit frustrating with the dying online, so you may want to concentrate on the missions (Multiplayer > Online > My Stuff > Missions) and fulfil some requirements there for some more FP. For instance just doing 100 donuts will get you 4350 FP alone. Also, finishing higher in populated lobbies will help more than winning races against one other person. Just keep going and you will eventually achieve this.