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