Here is the full list of all 51 Titanfall 2 trophies - there are 40 bronze, 8 silver, 2 gold and 1 platinum.
Viewed Anderson's first Holographic Log
Kill a Caged Prowler in the Wildlife Research Labs
Find 10 Collectibles
Defeated Ash
Destroy a Mercenary Titan with a melee execution in the Campaign
Destroy a Titan with your Flight Core in the Campaign
Destroy an enemy Titan as a Pilot in the Campaign
Defeated the Reapers in Ash's Simulation Dome
Climbed the Sideways Town
Entered the World Foundry
Defeated Kane
Fully Powered BT-7274
Join a multiplayer network
Customize a multiplayer loadout
Win a multiplayer match
Perform a melee takedown while cloaked in the Campaign
Completed training
Beat Pilot Anderson's Gauntlet ghost recorder time
Earned all trophies
Place in the top 3 on the Gauntlet scoreboard
Kept Lt. Shaver and Lt. Freeborn Alive
Completed Special Operation 217
Found the Arc Tool
Powered the Beacon
Retrieved a working Uplink Module
Defeated Richter
Used the Arc Tool to activate a Stalker rack
Located the Ark
Defeated Viper
Secured the Ark
Called in a new BT
Completed the rising world run
Defeated Slone
Destroy a Titan with your Burst Core in the Campaign
Destroy a Titan with your Salvo Core in the Campaign
Destroy a Titan with your Sword Core in the Campaign
Destroy a Titan with your Laser Core in the Campaign
Destroy a Titan with your Smart Core in the Campaign
Destroy a Titan with your Flame Core in the Campaign
Destroy 3 enemy Titans with 1 Core ability in the Campaign
Kill 25 infantry in 2 seconds as a Titan in the Campaign
Shoot and kill 3 enemies in a row while wallrunning as a Pilot in the Campaign
Shoot and kill 3 enemies in a row while sliding as a Pilot in the Campaign
Rodeo an enemy Titan in the Campaign
Acquire 6 or more friendly Stalkers at the same time in the Campaign
Complete the Campaign on Regular
Complete the Campaign on Hard
Complete the Campaign on Master
Collect all of BT's loadouts in the Campaign
Find 25 Collectibles
Find All Collectibles