Here is the full list of all 51 Sonic & All-Stars Racing Transformed trophies - there are 42 bronze, 5 silver, 3 gold and 1 platinum.
Earn every Trophy in the game
Raced in an ad hoc or Online game with Sonic, Tails, Amy, Shadow and Knuckles in the same race.
Manually select a Random character for a Matchmaking game
Win a Matchmaking game
Earn your Triple-Star License
Beat all the Staff Ghosts in Time Attack
Do 10 Stunt Combos in a single event
Get a Podium Finish in every Grand Prix tournament on Expert difficulty
Finish 1st in every Grand Prix tournament on Expert difficulty
Unlock every Character in the game
Get a Podium Finish in every Grand Prix tournament
Visit every location in the game
Earn your Star License
Unlock Mirror Grand Prix mode
Finish 1st in a Grand Prix tournament
Finish 1st in a Grand Prix tournament at Expert difficulty
Get a Perfect Drift score on a Drift Challenge event
Beat your first Staff Ghost in Time Attack
Beat 01:11.16 in Time Attack as Vyse in Rogue's Landing
Collect every Star in World Tour
Roll Left, Roll Right, Backflip, Forward Flip and land as a car or boat
Complete the Dream Valley Ring Race and pass every Ring as NiGHTS or Reala
Earn your S Class License
Score 90% accuracy with aimed weapons in an event
Freeze an opponent with Ice from at least 100 meters away
Complete a World Tour event on Expert difficulty
Unlock Superstar Showdown in World Tour
Do a Boost-Start in each vehicle mode
Earn your A Class License
Get a total of 20 hits with weapons in a Race
Do a 10 second Drift as Sonic
Triple-Stunt while transforming into a car or boat
Get 10 hits by firing weapons backwards in a single event
Hit 2 opponents with a single Hot Rod Blast
Absorb a weapon with the Glove and fire it back at your attacker
Finish a Battle Race without losing any lives
Hit 1st, 2nd and 3rd place with a Swarm attack
Survive a Twister attack without crashing or being hit
Do 5 overtakes in a single Drift
Hit an opponent with a weapon while looking backwards
Earn your B Class License
Do a Reckless Boost
Do a Level 3 Air-Drift
Evade or Block a homing-weapon 3 times in a Race
Detonate the Hot Rod at the very last second
Win an event with a Mod equipped
Collect 10 Stars in World Tour
Finish 1st in a Race without getting hit by weapons
Level-up a character
Finish 0.5 seconds ahead of an opponent in a Race
Go All-Star!