In order to earn this trophy, you will first need to unlock the "NFS Hero" license plate by unlocking all standard non-dlc mods for all 5 NFS Heroes pack cars. Only one of the NFS Heroes pack cars will be unlocked online at first. The other 4 unlock by completing events online with a sports car (for example the 350Z).
Nissan 350Z is unlocked from the start.
Complete 6 events in sports cars to unlock Nissan Skyline
Complete 12 events in sports cars to unlock Lamborghini Diablo S/V
Complete 18 events in sports cars to unlock Porsche 911 GT2.
Complete 24 events in sports cars to unlock Bmw M3 GTR
It is worth noting that the wins don't "reset", so you will unlock one car every 6 events you complete in sports cars. You can either do this normally online and get some mileage in as you will need it anyway, or you can grab a friend and do some quick events over and over again. A good event for this is located on the SW corner of downtown, a challenge called "Pyramid parking". Refer to the map below for the location of the event.
In order to unlock the "NFS Hero" license plate needed for NFS Hero: Hero Worship you will need to unlock every single non-dlc standard mod for all five cars. Every car will come with Burn Nitrous already unlocked. Track tires, Reinflates, Reinforced chassis, Short gears and Powershot nitrous will unlock via mileage. While the order varies, the last of them will always unlock upon reaching 200 miles driven.
The last 4 mods require specific tasks with specific upgrades equipped:
Impact protection body requires 10 takedowns with powershot equipped.
Long gears requires 5000 yards of drifting with track tires equipped.
Off-road tires unlock upon getting a total of 1500 yards of air with reinforced chassis equipped.
Aero body requires 60 near misses with short gears equipped.
All of these can be done in a private lobby by yourself besides impact protection body. At least Aero body and long gears should unlock naturally if you unlock and equip the related mod at the 100 miles mark or before.
There are few approaches to reach the 200 miles in each car:
1) Just play normally on speedlists, takes longer but if you like the game online then why not do so? If you do it like this, add 9 hours to the estimated time.
2) Drive round the main highway repeatedly. If you do it counterclockwise, there are less sharp turns and you can maintain a higher average speed. This is the quickest way but also the most boring way as well.
3) Find a suitable edge that will respawn your car upon driving down so that it's heading to the edge again. Tape R2 down. This is propably the least fun way but requires nearly zero effort. Add about 15 hours to the estimated time.
After you have the plate, equip it and win any type of event online. While this can be boosted, you shouldn't need to as you can use any car you wish and it will still unlock upon winning.
1 marks the "Pyramid parking" event for racking up events quickly.
2 marks the location for the drift required for the "Under control" plate.