Here is the full list of all 51 Injustice: Gods Among Us trophies - there are 38 bronze, 10 silver, 2 gold and 1 platinum.
Complete 1 S.T.A.R. Lab Mission
Defeat every Villain With Batman
Send an opponent through all three Metropolis transitions in one fight
Knock an opponent through a transition
Win with Batman using every special move and his Supermove
Make a comeback when at low health (10% or less)
Use every interactable and win in a multiplayer match
Win a match with Green Arrow using only arrows
Win a match as Deathstroke without missing a shot (minimum 12 shots)
Win a multiplayer match with a timeout
Perform 8 throws and win in a multiplayer match
Win all story mode minigames
View Your Hero Card
Equip a new Character Portrait
Equip a new Icon
Equip a new Background Image
Enter Practice Mode
Complete Tutorial
Complete Classic Battle with any character
Complete 100% of Story Mode
Win a match with the super move of any character
Complete 50% of Story Mode
Reach Level 10
Win a Clash sequence with any character
You've unlocked all Trophies!
Complete Classic Battle with all characters
Complete Battle Mode
Beat All S.T.A.R. Lab Missions (Excluding DLC)
Reach Level 100
Win a single online match
Dethrone the King in an online match
Vote Correctly in a KOTH match
Defeat a Survivor
Win 100 complete Online Matches
Play 200 complete Online Matches
Win 1 complete Ranked match
Win 10 complete Ranked matches
Enter Online Practice with someone on your friends list
Get 3 stars on 1 S.T.A.R. Lab Mission
Get 100 Stars in S.T.A.R. Lab Mode
Complete All S.T.A.R. Lab Missions with 3 Stars
Perform a 10 hit combo with every character
Knock opponent through all transitions across all levels
Perform every character's supermove
Perform every special move of every character
Perform every Meter Burn special move of every character
Perform every level interaction once
Unlock a costume in the Archives
Unlock All costumes in the Archives
Unlock everything in the Archives
Cause maximum damage in all Arenas (does not include Practice mode)