Here is the full list of all 50 Inversion achievements worth 1,000 gamerscore.
Be a part of a winning team in Assault Mode (Matchmaking)
Reach Silver Grav Sergeant Rank
Perform 10 Finishing Moves using High Grav Powers (Campaign)
Perform 50 Finishing Moves using High Grav Powers (Campaign)
Use the Gravlink to throw 50 Lutadore Enemies (Campaign)
Escape from a Lurker's grasp 5 times during single player
Kill 100 Lutadore Enemies with explosives in the Campaign (Grenades, Rockets, Barrels)
Use a Shotgun to gib 25 Lutadore enemies (Any Difficulty)
Be a part of a winning team in Team Deathmatch (Matchmaking)
Use the Gravlink to throw 30 Lutadore Enemies (Campaign)
Shoot off 100 Lutadore Helmets (Any Difficulty)
Finish the Campaign on Low Gravity Difficulty
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
Finish the Campaign with a Friend (Any Difficulty)
Defeat The Prophet Kiltehr (Any 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
Set 25 Lutadore enemies on fire with the Lavagun (Any Difficulty)
Defeat The Brute (Any Difficulty)
Use the Gravlink to throw 15 Lutadore Enemies (Campaign)
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
Perform 50 Finishing Moves using Low Grav Powers (Campaign)
Get 1st Place in a Deathmatch game (Matchmaking)
Complete the final checkpoint in Edge of the World on Normal or High Difficulty
Defeat The Slave Driver (Any Difficulty)
Complete the final checkpoint in Road to Hell on Normal or High Difficulty
Use the Gravlink to kill 3 Lutadores with one object (Campaign)
Use the Gravlink to kill 5 Lutadores with one object (Campaign)
Perform 10 Finishing Moves using Low Grav Powers (Campaign)
Complete the final checkpoint in Street Fight on Normal or High Difficulty
Defeat The Butcher (Any Difficulty)
Use the Gravlink to throw a corpse at your friend (Co-op mode)
Have a friend boost you over a ledge (Co-op mode)
Complete a Campaign level with a Friend (Any Difficulty)
Revive a friend online (Co-op mode)
Change your multiplayer character's appearance
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
Take the Gravlink from the Lutadores
Complete the final checkpoint in Vanguard Down on Normal or High Difficulty
Reach Bronze Grav Captain Rank
Reach Gold Grav Major Rank
Reach Diamond Grav Commander Rank
Complete All Multiplayer Weapon Challenges
Complete All Multiplayer Basic Challenges