There are 51 Trophies that can be collected.

Bronze

The Might of the Righteous
Kill 100 enemies.

Success is Measured in Blood
Kill 500 enemies using Melee weapons.

Angel of Death
Kill 500 enemies using Ranged weapons.

Firepower
Kill 250 enemies using Exotic weapons.

The Bigger They Are…
Kill 25 Ork Nobs.

Not So Tough
Kill 10 'Ard Boyz.

Glorious Slaughter
Kill 75 enemies using Executions.

Put Them Down
Get 100 Headshots.

Shock & Awe
Kill 150 enemies using the Charge attack.

Death from Above
Kill 25 enemies with Ground Pound.

The Emperor's Marksman
Kill 10 enemies in a row in a single Ranged Fury activation.

The Emperor Protects
Complete Part 1 of the game on Hard difficulty in a single session without dying or restarting.

Nob Down
Win 10 struggles against the Ork Nob.

Blast Radius
Multi-kill -- 5 enemies with 1 Frag grenade.

Precision Killer
Multi-kill -- 2 enemies with 1 Stalker-Pattern bolter shot.

Chain of Death
Multi-kill -- Detonate a chain of 5 consecutive Vengeance Launcher rounds, killing 10 enemies.

Master of Sword and Gun
Complete a Chapter of the single-player campaign using only the Bolt Pistol and Chainsword.

Burn Them All
Complete a Chapter of the single-player campaign using only Plasma weapons.

Brute Force…Unleashed
Complete a Chapter of the single-player game using only the Vengeance Launcher and Power Axe.

Finesse and Fury
Complete a Chapter of the single-player game using only Stalker-Pattern Bolter and Chainsword.

Lexicanum
Collect 10 Servo Skulls.

Battle Brother
Get a Multiplayer character to Lvl 10.

Veteran
Get a Multiplayer character to Lvl 20.

Captain
Get a Multiplayer character to Lvl 30.

Warrior of Darkness and Light
Play 10 Multiplayer games as Space Marine and 10 Multiplayer games as Chaos Marine.

Shapeshifter
Play each class in Multiplayer.

Jack of All Trades
Play 10 Multiplayer games using each class.

Master of Arms
Complete 5 weapon challenges.

Armored in Glory
Complete 10 armor challenges.

Defender
Kill 25 opponents who are capturing your Control Point in Seize Ground.

Devastation!
Have 10 times more kills than deaths in a single game of Annihilation.

Master Crafted
Fully customize a Space Marine and a Chaos Space Marine character.

Down to Earth
Kill 50 Assault Marines/Raptors in mid-air.

Silver

Visible, Violent Death
Kill 2500 enemies.

Master of the Clean Kill
Get 250 Headshots.

Feel My Wrath
Kill 250 enemies using Melee Fury attacks.

Chapter Master
Get a Multiplayer character to Lvl 40.

Keeper of the Armory
Complete all the weapon challenges.

Gold

None Can Stand Before You
Complete the entire game on Hard difficulty.

Librarian of Macragge
Collect all Servo Skulls.

True Son of the Emperor
Kill 40,000 enemies in the game (all game modes combined).

Platinum

Trophy Collection Complete
Collect all of the Warhammer 40,000: Space Marine trophies.

9 Secret

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