Here is the full list of all 51 Inversion trophies - there are 38 bronze, 10 silver, 2 gold and 1 platinum.
Unlock all trophies
Complete All Multiplayer Basic Challenges
Reach Diamond Grav Commander Rank
Shoot off 100 Lutadore Helmets (Any Difficulty)
Use a Shotgun to gib 25 Lutadore enemies (Any Difficulty)
Kill 100 Lutadore Enemies with explosives in the Campaign (Grenades, Rockets, Barrels)
Use the Gravlink to throw 50 Lutadore Enemies (Campaign)
Use the Gravlink to throw 30 Lutadore Enemies (Campaign)
Use the Gravlink to throw 15 Lutadore Enemies (Campaign)
Perform 50 Finishing Moves using High Grav Powers (Campaign)
Set 25 Lutadore enemies on fire with the Lavagun (Any Difficulty)
Defeat The Brute (Any Difficulty)
Perform 10 Finishing Moves using High Grav Powers (Campaign)
Escape from a Lurker's grasp 5 times during single player
Use the Gravlink to kill 5 Lutadores with one object (Campaign)
Use the Gravlink to kill 3 Lutadores with one object (Campaign)
Defeat The Butcher (Any Difficulty)
Perform 50 Finishing Moves using Low Grav Powers (Campaign)
Perform 10 Finishing Moves using Low Grav Powers (Campaign)
Take the Gravlink from the Lutadores
Finish the Campaign on Normal Gravity Difficulty
Finish the Campaign on High Gravity Difficulty
Complete the final checkpoint in Reversion on Normal or High Difficulty
Complete the final checkpoint in Deja Vanguard on Normal or High Difficulty
Complete the final checkpoint in Red Sky on Normal or High Difficulty
Complete the final checkpoint in Reveal on Normal or High Difficulty
Complete the final checkpoint in Enlightenment on Normal or High Difficulty
Complete the final checkpoint in Into the Depths on Normal or High Difficulty
Complete the final checkpoint in Edge of the World on Normal or High Difficulty
Complete the final checkpoint in Road to Hell on Normal or High Difficulty
Complete the final checkpoint in Street Fight on Normal or High Difficulty
Complete the final checkpoint in Road Home on Normal or High Difficulty
Complete the final checkpoint in Breakout on Normal or High Difficulty
Complete the final checkpoint in Caged on Normal or High Difficulty
Complete the final checkpoint in Vanguard Down on Normal or High Difficulty
Be a part of a winning team in Assault Mode (Matchmaking)
Complete All Multiplayer Weapon Challenges
Reach Gold Grav Major Rank
Finish the Campaign on Low Gravity Difficulty
Finish the Campaign with a Friend (Any Difficulty)
Defeat The Prophet Kiltehr (Any Difficulty)
Have a friend boost you over a ledge (Co-op mode)
Defeat The Slave Driver (Any Difficulty)
Use the Gravlink to throw a corpse at your friend (Co-op mode)
Complete a Campaign level with a Friend (Any Difficulty)
Revive a friend online (Co-op mode)
Be a part of a winning team in Team Deathmatch (Matchmaking)
Reach Bronze Grav Captain Rank
Reach Silver Grav Sergeant Rank
Change your multiplayer character's appearance
Get 1st Place in a Deathmatch game (Matchmaking)