Takedown an opponent with 'Ultimate Fan' as your License Plate (Multiplayer)
Unlocking the cars
First, the new cars need to be unlocked for use in multiplayer. This is done by completing Speedlist events in Exotic cars. Winning is not required, and can be done in public or private games. A Speedlist consists of 5 events, so this can be done after playing 5 Speedlists. The requirements for each car are as follows:
Pagani Zonda R - Automatically Available
Bugatti Veyron Grand Sport Vitesse - Complete 6 events in Exotics.
Lamborghini Aventador J - Complete 12 events in Exotics.
Mclaren F1 LM - Complete 18 events in Exotics.
Hennesey Venom GT Spyder - Complete 24 events in Exotics.
If you're doing it in a friends game, a quick method is to create a custom Speedlist and selecting the "Arch Angels" challenge 5 times. It's a Park Up event, and it takes place the same place as the meetup. Because of this, you can sit in one spot the entire Speedlist and complete all 5 events without any effort. The event takes about 30 seconds each time.
Unlocking the license plate
The 'Ultimate Fan' license plate is unlocked by unlocking all Standard Mods on all 5 of the Ultimate Speed Pack cars in multiplayer. This can be a bit of a grind because it involves driving 200 miles in each car. All mods can be unlocked in a private game by yourself, with the exception of Impact Protection, which requires 10 takedowns. The requirements for unlocking mods are unchanged in the DLC, and are as follows:
Lightweight - Get 60 Near Misses with Short Gears equipped.
Reinforced - Drive 200 miles.
Aero - Drive 5 miles.
Impact Protection - Get 10 takedowns with Powershot equipped.
Long Gears - Drift 5,000 yards with Track Tires equipped.
Short Gears - Drive 10 miles
Once "Ultimate Fan" is unlocked, choose that as your license plate. Find another player and score a takedown to unlock the achievement.
Find players to boost takedowns in the Achievement Trading Thread. For driving 200 miles, you can start a drift in a big open area like the airfield, then rubber band/tape your controller and increase your driving distance while you do something else. Be sure to have at least reinflates equipped because your tires are prone to popping. Donuts work too, but will obviously be slower. Also note, if you're using a wireless controller it'll still disconnect after a few minutes of inactivity.
An easy method for accumulating 200 miles is to drive off a cliff. In some areas, your car respawns facing the cliff and cause you to roll off the cliff repeatedly, allowing you to increase driving distance while you're away from the game. Rubber banding the controller isn't required, but can make it slightly faster. It takes about 4 hours to accumulate 200 miles this way.