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 Classic Battle with any character
Cause maximum damage in all Arenas (does not include Practice mode)
Get 3 stars on 1 S.T.A.R. Lab Mission
Complete 1 S.T.A.R. Lab Mission
Win a Clash sequence with any character
Win with Batman using every special move and his Supermove
Equip a new Background Image
Unlock All costumes in the Archives
Unlock a costume in the Archives
Complete 100% of Story Mode
Win all story mode minigames
Complete 50% of Story Mode
Make a comeback when at low health (10% or less)
Win a single online match
Enter Online Practice with someone on your friends list
Enter Practice Mode
Reach Level 10
View Your Hero Card
Equip a new Character Portrait
Equip a new Icon
Win a match with the super move of any character
Send an opponent through all three Metropolis transitions in one fight
Knock an opponent through a transition
Complete Tutorial
You've unlocked all Trophies!
Complete Classic Battle with all characters
Complete Battle Mode
Perform 8 throws and win in a multiplayer match
Use every interactable and win in a multiplayer match
Win a multiplayer match with a timeout
Beat All S.T.A.R. Lab Missions (Excluding DLC)
Reach Level 100
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
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
Win a match with Green Arrow using only arrows
Perform every level interaction once
Defeat every Villain With Batman
Win a match as Deathstroke without missing a shot (minimum 12 shots)
Unlock everything in the Archives