Successfully complete one of the following tasks to get a trophy:

The first stage of the podium (Bronze): Win your first race.
The roar of the Jaguar (Bronze): Win a race using one of the Jaguar of the Ferlito Motors team.
Girl Power (Bronze): Win a race using Maria De Villota.
Race of Good Hope (Bronze): Win a race on Kyalami with Francesco Ascani.
It's raining cats and...jaguars? (Bronze): Win a race on Magione with wet weather using the Ferlito Motors Jaguar.
The sunny side of the street (Bronze): Win a race on Valencia on sunny weather using the SSantucci Motorsport Mustard.
The rainy side of the street (Bronze): Win a race with wet weather in any game mode.
The driver more than the car (Bronze): Win at least a race with every team in the game.
I like simulation (Bronze): Win a race in simulation mode at Legend difficulty level.
Komodo Dragon (Bronze): Win a race in Varano at Hard or Legend difficulty level.
Speed Temple (Bronze): Win a race on Monza at Legend difficulty level.
All roads lead to Rome (Bronze): Win a race on Vallelunga Track.
Gear Power (Bronze): Win a race using manual transmission.
Unrivaled (Bronze): Win a race with a 15 seconds gap or more from the second place.
Smells like burnt rubber (Bronze): Win a race performing 10 seconds of powerskid.
The first of a long series (Bronze): Complete one of the challenges of the Superstars Licenses Mode.
Mister Tester (Bronze): Complete 15 laps in Training Mode with the same driver.
I'm in love with my car (Bronze): Drive for at least 200 km in Single Player mode with the same team.
A present for you! (Bronze): Unlock a Prize.
Superstars veteran (Silver): Win at least 10 races.
Mister Pole Position (Silver): Achieve at least 8 Pole Positions in the same championship.
A new danger on the track (Silver): Complete all the Special Trials challenges.
The Final Countdown (Silver): Complete all the Countdown challenges.
Owned! (Silver): Complete all the Duels challenges.
Not a comedy (Silver): Complete all the Race Scenarios challenges.
The king of hourglass (Silver): Beat at least 8 different records in Training.
International Series (Silver): Win the race of Vallelunga, Mugello, Monza and Valencia during the same championship.
Ave Cesari (Silver): Win 5 races on Vallelunga with Mauro Cesari.
No more space on the shelf (Silver): Unlock all the championship and track cups.
Congratulations from the Designer (Gold): Complete all the challenges at Platinum level.
Audi famam illius (Gold): Win a Championship with Gianni Morbidelli and his Audi car.
BMWinner (Gold): Win a championship with CAAL Racing team at least at Medium difficulty.
The best around (Gold): Win a championship at Legend difficulty level.
You are a Platinum Superstar! (Platinum): Collect all Trophies.

Additionally, there is one secret trophy:

Secret trophy (Unknown): Unknown.