Here is the full list of all 34 Matterfall trophies - there are 20 bronze, 8 silver, 5 gold and 1 platinum.
Earn All Trophies
Complete a level without equipping any Augmentations
Get the max speed bonus in all levels on Master difficulty
Defeat all bosses on Master difficulty
Get through the Research Labs Zero-G sections without taking damage
Destroy 20 enemies with a Matter Bomb
Collect all Caches in Matter Mines
Get a multiplier of 20x on Freelancer difficulty
Keep your Overcharge going for a full 10 seconds
Get a multiplier of 10x on Rookie difficulty
Complete a level without firing a weapon
Collect all Caches in Fortuna City
Kill an enemy in a level with each of the Secondary weapons
Save all civilians in Fortuna City and defeat the chapter Boss
Destroy 35 enemies during one Overcharge
Stun 10 Missile enemies in one Strike
Collect all Secondary weapons
Equip Secondary weapons in all slots
Achieve a no-death bonus on every level, on Veteran difficulty
Complete all levels on Veteran difficulty
Complete all levels on Freelancer difficulty
Complete all levels on Rookie difficulty
Complete the Matter Mines chapter
Save all civilians in Matter Mines and defeat the chapter Boss
All Augmentations collected
Complete the Hydroponics chapter
Save all civilians in Hydroponics and defeat the chapter Boss
Collect all Caches in Hydroponics
Blow up 5 Matter Bombs by activating only one
Stun 8 enemies with a single Strike
Complete the Fortuna City chapter
Get a multiplier of 30x on Veteran difficulty
Rescue 5 civilians
Ride the Elevator in Boulevard Concourse