Here is the full list of all 51 Lost Planet 3 trophies - there are 38 bronze, 10 silver, 2 gold and 1 platinum.
Finished the Game on Any Difficulty.
Stopped Isenberg for Good.
Watched Coronis Fall.
Defeated Laroche.
Discovered Nushi.
Restored the Fueling Depot.
Killed the Gorevorgg.
Found all Mementos.
Found a Memento.
Took Storm Readings.
Completed Deep Core Drilling.
Tagged an Albino Tarkaa.
Stopped the Akrid infestation.
Opened the Armory.
Returned the Medicine.
Killed a Cat-G Akrid with the Rig.
Found 50% of Logs.
Found a Mysterious Structure.
Brought the Com-Dish Online.
Purchase First Rig Upgrade.
Planted your First T-Post.
Rescued the Trapped Scientists.
First Weapon Upgrade Purchased.
Secured the Moorings.
Emptied your First T-Post.
Defended Laroche.
Got your Rig.
Found a Log.
Saved by Laroche.
Unlock all Trophies.
Finished the Game on Hard Difficulty.
Planted every Post.
Bought every Weapon and Rig Upgrade.
Fully Unlocked Bestiary.
Found all Logs.
Finished Kovac's Quests.
Purchased all Ethologist Upgrades.
Discovered the Lost Contractor's Fate.
Won a Multiplayer Match.
Won 25 Multiplayer Matches.
Won every Scenario.
Perform your first Stealth Kill in a Multiplayer Game.
Delivered The T-Eng Canister 2 times during a multiplayer Outpost Scenario match.
Killed 20 Wardeyes during a multiplayer Research Lab Akrid Survival match.
Delivered the T-Eng Canister 3 times during a multiplayer Alpha Lair Scenario match.
Destroyed Satellite Array.
Get a kill while on the Battlecat.
Delivered the T-Eng Canister to win a multiplayer Quarantine Scenario match.
Unlocked Sphere Cell.
Unlocked 30 Sphere Cells.
Unlocked all Sphere Cells.