Here is the full list of all 38 Warhammer 40,000: Deathwatch trophies - there are 16 bronze, 19 silver, 2 gold and 1 platinum.
Earn all trophies
Complete a mission on Heroic difficulty without a Space Marine being killed
Complete a mission on Veteran or Heroic difficulty without a Space Marine taking damage
Collect everything in the Codex
Collect all Space Marines
Collect all non-Weapon Wargear
Collect all Weapons
Collect all Ultramarines' Space Marines and Wargear
Collect all Blood Angels' Space Marines and Wargear
Collect all Space Wolves' Space Marines and Wargear
Collect all Miscellaneous Wargear
Collect all Shields
Collect all Purity Seals
Collect all Grenades
Collect all Lascannons
Collect all Missile Launchers
Collect all Melee Weapons
Collect all Grav Guns
Collect all Melta Weapons
Collect all Flame Weapons
Collect all Plasma Weapons
Collect all Bolt Weapons
Complete 'Longest Day' without triggering any mines
Complete a mission on Veteran or Heroic difficulty, using only Tier 1 Space Marines with no additional Wargear
Enter a mission with a squad of Space Marines who have all of their abilities unlocked, and Wargear in every Wargear slot
Collect a Tier 4 Wargear
Survive a shot from an Impaler Cannon
Level a Space Marine to Level 10
Level a Space Marine to Level 25
Level a Space Marine to Level 50
Unlock all of a Space Marine's abilities and traits
Raise a Space Marine's Accuracy to 100%
Raise a Space Marine's Crit to 50%
Raise a Space Marine's HP to 400
Kill a Carnifex without it spending any AP
Kill one of each large Tyranid
Kill 40,000 Tyranids
Complete a mission without attacking