Here is the full list of all 51 MotoGP 13 trophies - there are 38 bronze, 10 silver, 2 gold and 1 platinum.
Unlock all Trophies
Reach 3 hours of race time in valid Online Matches
Complete a Championship based on the official calendar in a better position than Valentino Rossi
Win a race as B. Spies on the Circuit of the Americas
Ride for at least 1000 km (622 miles) in any offline game mode
Reach a total of 60 min. of race time in valid Online Matches
Go to the track and use a rewind
Sign a contract in Career mode with Ducati Team, Repsol Honda Team or Yamaha Factory Racing
Perform a total 2 minutes in endos
Spend a total of 2 minutes doing wheelies
Complete an Online Championship
Complete an Online Grand Prix
Reach GP Level 40
Earn 1000000 fans in Career mode
Win a MotoGP™ race with one of these bikes: ART, FTR, FTR Kawasaki, FTR Honda, Suter, PBM
Win a race as N. Hayden on Laguna Seca
Win a race as D. Pedrosa on Motegi
Complete one valid race on each track in the game
Win a race as V. Rossi on Laguna Seca
Win a race as J. Lorenzo on Mugello
Win a race on a Spanish track with a Spanish rider
Win a race on an Italian track with an Italian rider
Achieve a Pole Position, the Fastest Lap and win the Race on the same offline Weekend
Start an offline race from the Pole Position
Select the Pro Physics level in Riding Aids and complete a race
Reach 300 km/h (187 mph) in any game mode
Sign your first contract in MotoGP™ class in Career mode
Reach GP Level 25
Reach GP Level 20
Reach GP Level 15
Be featured on the "Bike Today" newspaper cover in Career mode
Win a Rider Championship in any class in Career mode
Reach GP Level 10
Raise your GP Level in order to unlock a team
Enter the Bike Settings menu in the Pit
Reach GP Level 5
Win in rainy conditions (Rain or Light Rain)
Raise your GP Level in order to unlock a rider
Earn 40000 fans in Career mode
Earn 20000 fans in Career mode
Win a race starting from the last position
Perform the fastest lap in an offline race
Raise your GP Level in order to unlock a helmet
Enter the Replay mode for the first time
Complete a Team objective in Career mode
Use the Technical Meeting in the Pit to change your bike settings
Change your rider's helmet in Rider Customization section
Enter your Social Feeds page in Career mode
Race using the Helmet view
Sign your first contract in Career mode
Create your first custom rider