Here is the full list of all 41 Assetto Corsa Competizione trophies - there are 22 bronze, 15 silver, 3 gold and 1 platinum.
Completed 10 valid laps in Hotlap mode
Go 280km/h
Stay in an opponent's slipstream for 5 seconds
Achieve a session Consistency Rating of 99 (NB: very difficult to acquire)
Achieve Bronze driver category
Drive your first lap at Spa
Take part in a Multiplayer race
Complete 5 clean laps in a row (do not cut, lose control, or go too slow)
Earn a track medal on any track in the GT World Challenge
Earn all medals on a single track in the GT World Challenge
Earn all medals for all tracks in the GT World Challenge
Achieve Silver driver category
Begin to learn a track
Go 150km/h
This is the platinum trophy and is unlocked automatically when all the trophies have been unlocked
Drive for two hours in a session
Drive more than 100km in one session
Complete 10 clean laps in a row (do not cut, lose control, or go too slow)
Complete a Championship
Complete the Career mode
Complete 10 laps in Practice mode with all driving assists turned off
Try every car and track in the GT World Challenge
Win a race with every car in the GT World Challenge
Take part in a night race
Lap every opponent at least once within a single race (minimum 15 opponents)
Win a race from the back of the grid (minimum 10 cars)
Stay in first place for the entire race (minimum 10 cars)
Complete a lap at Spa in under 2:25
Get on a Special Event leaderboard
Complete a race without damages (Valid hotlap speeds, 10 cars minimum, not disqualified)
Receive your first penalty
Start in pole position in any race (Earned from a qualifying session)
Totally destroy your car
Break your car's engine
Get pole, fastest lap, and race win in the same race (Pole from qualifying and 15 opponents minimum)
Complete a Short Career achieving a gold cup
Complete a Medium Career achieving a gold cup
Complete a Long Career achieving a gold cup
Win a Championship
Achieve Gold driver category
Achieve Platinum driver category