The fourth event is a standard Rallycross race on the Los Angeles track.
I recommend taking your Joker Lap on lap 1/3 in order to get it out of the way. The Delta Integrale 8v you drive in this event is a powerful 4WD and a good car in my opinion. The only problem is that all your opponents are driving them as well.
I find a bit of dirty racing is the way to get ahead the fastest on the Los Angeles track, as the lack of long straights makes it difficult to capitalize on the AI's conservative driving. If you start braking shortly after the car in front of you, you can pass them in the corner and use their car to help you around the corner.
Simply come in 1st after the three laps (and one joker lap) for the achievement.