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