For this trophy, you need to complete a few specific tasks online with the new Nissans, the 350Z and Skyline. In order to unlock the Skyline you will need to complete 6 events online in sports cars (for example, the 350Z).
Plates and their related tasks:
Under Pressure: Win a race or team race in the 350Z without being overtaken.
Simple enough, yet not too easy. The Nissan 350Z is quite slow compared to the Bugatti Veyron for example. You just need to lead a race from start to finish for this to unlock. Can be boosted in a private lobby with one friend.
Under Attack: Complete a speed test in the 350Z without being eliminated.
You get eliminated in a speed test if you get taken down. Wrecking doesn't count. You don't need to win so you can just drive far away from other players to avoid being eliminated. You can complete this one in a private lobby with one friend if you'd rather boost.
Under Control: Record a 383 yard drift in the 350Z inside the Foley Street parking garage spiral.
Refer to the map in NFS: Hero Worship for the location. In said car park there is a spiral from the bottom to the very top. You get just around 383 yards if you drift it in one go. I got this to unlock with 360 or so, the most important thing seems to be you drifting it in one go. In my opinion it's easier from the bottom to the top, but either way should count. Can be done alone in a private lobby.
Under The Influence: Drive on rims for one mile during speedlists in the Nissan Skyline.
While you are in a speedlist (any time in a public lobby will count except intermission) you need to first pop the tires, then drive for a mile on rims. This doesn't have to be on one go. To pop the tires, hold + until your rear tires pop out. Now you can start getting the distance in. Can be boosted in a private lobby with a friend.
Under Your Skin: Takedown the same player five times in a row in the Nissan Skyline.
For this you need to get five takedowns in a row (so no wrecking in between) and it has to be the same player every time. You can naturally try your luck in public lobbies, however this one is more reasonable to boost with one friend in a private lobby.
Under The Influence: Eliminate at least 2 opponents in a speed test in Nissan Skyline.
Eliminating a player from a speedtest is done by taking them out (without wrecking yourself). The Skyline isn't a terribly good car for wrecking people out, if you manage to get instant takedowns active during a test it will make this one much easier. You can be eliminated from the test yourself and still unlock this. However, this would be very easy to unlock if you get two friends into a private lobby to help you.
After all 6 are unlocked, the trophy will pop shortly afterwards.