Here is the full list of all 52 Team Sonic Racing trophies - there are 40 bronze, 9 silver, 2 gold and 1 platinum.
Perform a maximum Start Line Boost.
Complete Chapter 1 of Team Adventure Mode.
Complete all possible events on hard in any Team Adventure Mode chapter.
Perform 100 Team Slingshots. (Across all Game Modes).
Perform 10 Team Slingshots in a single Race.
Block an incoming projectile with a Blue Cube.
Send an Item Box to a Teammate 5 times during a Race.
Use the White Boost to destroy a projectile.
Cause an opponent to spin-out using a Red Burst.
Perform Team Item Transfer, Skimboost, Team Slingshot and Team Ultimate in a single Race.
Beat a friend's leaderboard time in Time Trial mode on any track.
Modify a vehicle in the Garage.
Come first in an online race.
Finish an online race.
Perform a triple Stunt.
Perform a Skimboost on a slow-moving Teammate.
Collect all Trophies.
Complete Chapter 2 of Team Adventure Mode.
Complete Chapter 3 of Team Adventure Mode.
Complete Chapter 4 of Team Adventure Mode.
Complete Chapter 5 of Team Adventure Mode.
Complete Chapter 6 of Team Adventure Mode.
Complete Chapter 7 of Team Adventure Mode.
Earn every star in Team Adventure Mode Chapter 1.
Earn every star in Team Adventure Mode Chapter 2.
Earn every star in Team Adventure Mode Chapter 3.
Earn every star in Team Adventure Mode Chapter 4.
Earn every star in Team Adventure Mode Chapter 5.
Earn every star in Team Adventure Mode Chapter 6.
Earn every star in Team Adventure Mode Chapter 7.
Earn every star in Team Adventure Mode.
Collect all of the Team Adventure Mode Keys.
Complete all Team Adventure chapters on Hard difficulty.
Gain 6 positions by using a single Yellow Drill.
Stay in a single Drift for over a minute.
Collect 20,000 Rings.
Travel 200 meters over slow-down surfaces with a single use of a Jade Ghost.
Spend 5,000 Credits.
Spin out 2 racers with Cyan Laser.
Finish Frozen Junkyard without hitting any hazards or respawning.
Unlock all of the Performance Mods (Except Legendary Mods).
Unlock all of the Vehicle Paint Kits.
Perform a Team Ultimate 3 times in a single Race.
Land a hit on enemy racers with each use of a x3 Orange Rocket.
Use the White Boost to avoid being slowed down by terrain.
Use the Violet Void to absorb a projectile and hit the racer who fired it.
Cause 3 opponents to spin-out by shunting them with a Pink Spikes active.
Complete a Team Race with 2 additional local players on your Team.
While playing as Eggman, spin out Sonic 3 times in the same Race.
Avoid every hazard created by a Gray Quake.
Achieve 1st place in a race with a fully customized Vehicle.
Avoid the effect of being hit by an Ivory Lightning.