Here is the full list of all 46 MotoGP13 achievements.
Reach 300 km/h in any game mode
Race using the Helmet view
Enter the Bike Settings menu in the Pit
Create your first custom rider
Sign your first contract in Career mode
Enter your Social Feeds page in Career mode
Earn 40000 fans in Career mode
Complete a Team objective in Career mode
Earn 20000 fans in Career mode
Reach GP Level 5
Reach GP Level 10
Complete one valid race on each track in the game
Spend a total of 2 minutes doing wheelies
Perform a total 2 minutes in endos
Raise your GP Level in order to unlock a team
Raise your GP Level in order to unlock a helmet
Raise your GP Level in order to unlock a rider
Change your rider's helmet in Rider Customization section
Use the Technical Meeting in the Pit to change your bike settings
Perform the fastest lap in an offline race
Select the Pro Physics level in Riding Aids and complete a race
Go to the track and use a rewind
Win in rainy conditions (Rain or Light Rain)
Win a race on an Italian track with an Italian rider
Win a race on a Spanish track with a Spanish rider
Enter the Replay mode for the first time
Come in 1st and 2nd as B. Spies and C. Edwards at Austin while in the Split Screen mode
Win a MotoGP™ race with one of these bikes: ART, FTR, FTR Kawasaki, FTR Honda, Suter, PBM
Win a race as J. Lorenzo on Mugello
Win a race as V. Rossi on Laguna Seca
Win a race as D. Pedrosa on Motegi
Win a race as N. Hayden on Laguna Seca
Win a race as B. Spies on the Circuit of the Americas
Reach GP Level 20
Start an offline race from the Pole Position
Be featured on the "Bike Today" newspaper cover in Career mode
Earn 1000000 fans in Career mode
Sign your first contract in MotoGP™ class in Career mode
Sign a contract in Career mode with Ducati Team, Repsol Honda Team or Yamaha Factory Racing
Reach GP Level 25
Ride for at least 1000 km (622 miles) in any offline game mode
Achieve a Pole Position, the Fastest Lap and win the Race on the same offline Weekend
Win a race starting from last position
Reach GP Level 40
Win a Rider Championship in any class in Career mode
Complete a Championship based on the official calendar in a better position than Valentino Rossi