When you head online, only the Ford Fiesta ST will be unlocked at first. The rest of the cars will unlock by completing races on everyday cars, such as the Fiesta, Focus or Impreza.
Complete 6 events to unlock Alfa Romeo Mito QV
Complete 12 events to unlock BMW 1 Series M
Complete 18 events to unlock Audi RS3 Sportback
Complete 24 events to unlock Porsche 918 Spyder
You can either complete the events normally in public lobbies, or create a private lobby, grab a friend and do a suitable quick event repeatedly. A good event for this is "Pyramid parking" located in the southwest part of downtown. Check the map at the end of this section for the exact location. After you have these unlocked, you will need to unlock all of the 3 new mods on all of the cars.
Drift tires unlock by scoring 20, 200 yard+ drifts.
Jump nitrous unlocks by smashing 50 billboards (don't have to be unique, you can keep on crashing the same billboard if you so wish).
Ram chassis unlocks by driving 10 miles on oncoming.
These can be done in a private lobby on your own.
For the first two, i recommend heading to the new airport that this pack added. There are plenty of good billboards to crash. I kept on driving back and forth on the main runway and smashing the 2 billboards on the plane jump there. There is also a lot of room for the drifts. Ram chassis is fastest to complete by driving on the main highway.
After you have all the mods, the trophy won't unlock even though it should. Unlock any additional mod on any car and it will unlock. Credit: Boxster17