Here is the full list of all 51 Quantum Theory trophies - there are 42 bronze, 5 silver, 3 gold and 1 platinum.
Obtain all trophies.
Clear the entire story using only the Revenant.
Land 200 combo throws.
Clear the entire game on Hard.
Defeat Diablosis Soma (Thanatos III) on Hard in 3 minutes 30 seconds or less.
Clear Cavitas Cranii on Hard.
Defeat Chaos (Thanatos II) on Hard in 1 minute 30 seconds or less.
Kill the Raven on Hard in 2 minutes or less.
Shoot down 10 projectiles from the Raven.
Kill the Dreadnought on Hard in 2 minutes or less.
Kill 10 enemies with every firearm Syd can equip. (Melee kills don't count.)
Defeat Thanatos on Hard in 1 minute 30 seconds or less.
Clear The Womb on Hard.
Clear Lumenosynthetic Reactor 2 on Hard.
Land 100 full combo attacks. (3 consecutive hits)
Kill the Chariot during Thorax on Hard in 1 minute 30 seconds or less.
Clear Trachea on Hard.
Kill the Gargantua on Hard in 2 minutes 30 seconds or less.
Kill all enemies in Trachea without dying.
Destroy 50 Watchers. (50/50)
Kill 1000 enemies.
Clear The Root of the Tower on Hard.
Shoot an enemy with a Plasma Lancer from 50m.
Clear The Seed of Gnosis.
Clear Cavitas Cranii.
Kill 100 enemies with melee attacks using the Bloodcleaver.
Kill 200 enemies with headshots.
Clear The Womb.
Don't let any teammates who were setting charges go down during the final battle in The Womb.
Kill 500 enemies.
Hit 5 enemies with one shot from the Ifrit.
Clear Lumenosynthetic Reactor 2.
Destroy 20 Watchers. (20/50)
Filena killed 50 enemies.
Clear Trachea.
Obtain the rank of Immortal.
Clear The Root of the Tower.
Destroy 1 Watcher. (1/50)
Obtain the rank of Storm.
Obtain the rank of Berserker.
Obtain the rank of Slayer.
Obtain the rank of Elite.
Revive 10 teammates in one match.
Kill all members of the opposing team alone. (8-player Team Battle)
Kill all other players in an 8-player Deathmatch.
Obtain the rank of Commando.
Obtain the rank of Mercenary.
Obtain the rank of Soldier.
Obtain the rank of Novice.
Kill 20 opponents in one match.
Kill 10 opponents in a row during one match.