Here is the full list of all 51 Moto Racer 4 trophies - there are 37 bronze, 12 silver, 1 gold and 1 platinum.
Win all the trophies
Succeed a challenge
Unlock the eleventh chapter
Unlock 165 stars
Succeed chapter 5
Succeed 55 challenges
Do 250 wheelies
Do 3500 wheelies
Do 200 swerves
You knocked down 100 riders with swerves
Reach a total of 180 seconds of slipstreaming during a race
Keep your light trail for 120 seconds
Perform a whip on a dirt bike
Do a trick
Do a double flip
Score more than 800 points with a single trick
Reach a total of one hour in mid-air
Do a 250-meter drift
Successfully attempt 50 perfect landings in one race
Successfully attempt 200 orange T.U.R.B.O boosts
Score more than 5 000 000 style points
Win all races in the 6-5 Championship with Amund
Win the 6-2 challenge with a Gold performance
Upgrade Wrench and Bolt's bikes to the max
Score 3000 high-speed points in one go
Win the 9-3 challenge with a Gold performance
Customize Stella to the max
Successfully perform 200 T.U.R.B.O landings
Win the 3-3 challenge without using the turbo
Upgrade the T.U.R.B.O on Jody and Saul's bikes to the max
Succeed all the slalom challenges with 3 stars
Reach a total of 50,000 style points in one race
Reach a total of 150,000 style points in one race
Reach a total of 500,000 style points in one race
Reach a x10 style combo
Do a 5-second burn out… and win!
Do a 10-turn donut
Find all the shortcuts in the game
Ride on a truck's trailer
Move from one bridge to another over Spider Gorges
Land on an opponent and make him or her fall down
Do a wheelie on the Great Wall of China
Win a ten-player online game
Win 10 races online
Win a ten-player online championship
Finish a private online game
Make 10 online opponents fall down
Do a Flip + Trick combo
Brush against vehicles in traffic 300 times
Play a ten-player game
Finish a race 10s ahead of your nearest rival (single race - 'God' difficulty)