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