Here is the full list of all 51 Injustice: Gods Among Us Ultimate Edition trophies - there are 38 bronze, 10 silver, 2 gold and 1 platinum.
Knock opponent through all transitions across all levels
Defeat every Villain With Batman
Complete Tutorial
Get 3 stars on 1 S.T.A.R. Lab Mission
Win with Batman using every special move and his Supermove
Win a match as Deathstroke without missing a shot (minimum 12 shots)
Send an opponent through all three Metropolis transitions in one fight
Knock an opponent through a transition
Complete 1 S.T.A.R. Lab Mission
Search for an Adhoc match
Win a match with Green Arrow using only arrows
Win a match with Scorpion
Enter Practice Mode
Equip a new Background Image
Equip a new Icon
Equip a new Character Portrait
Unlock a costume in the Archives
Unlock All costumes in the Archives
Cause maximum damage in all Arenas (does not include Practice mode)
Complete Classic Battle with any character
View Your Hero Card
Complete 100% of Story Mode
Complete 50% of Story Mode
Reach Level 10
Using only the screen (touchscreen), complete one touchscreen minigame
Win a match with the super move of any character
Win a Clash sequence with any character
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)
Win all story mode minigames
Reach Level 100
Win a single online match
Using only the screen (touchscreen), complete all touchscreen minigames
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
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
Make a comeback when at low health (10% or less)
Unlock everything in the Archives