Here is the full list of all 40 The House of the Dead: OVERKILL Extended Cut trophies - there are 24 bronze, 11 silver, 4 gold and 1 platinum.
Complete all levels in Director's Cut
Maintain a Goregasm for 2 minutes
Collect 17 comic book pages
Complete any level in Director's Cut without using any continues
Complete any level with only one health segment remaining
Play each minigame through to completion once
Achieve a Goregasm
Complete any level with the targeting crosshair off
Complete all levels in Story Mode
Complete "Jailhouse Judgment" in Story Mode
Kill 5 or more mutants with one grenade
Collect 15 posters
Collect 10 LPs
Complete "The Fetid Waters" in Story Mode
Kill 100 mutants "Gangster Style" (holding gun sideways)
Collect 15 figurines
Buy a new weapon
Complete "Scream Train" in Story Mode
Decapitate 200 mutants
Fully upgrade any weapon
Complete "Creeping Flesh" in Story Mode
Complete "Carny" in Story Mode
Complete a level without triggering an enforced reload (i.e. reaching zero bullets)
Complete "Ballistic Trauma" in Story Mode
Complete "Naked Terror" in Story Mode
Complete "Papa's Palace of Pain" in Story Mode
Unlock all trophies
Complete all CHALLENGES for "Papa's Palace of Pain"
Complete all CHALLENGES for "Naked Terror"
Complete all CHALLENGES for "Ballistic Trauma"
Complete all CHALLENGES for "Carny"
Complete all CHALLENGES for "Creeping Flesh"
Complete all CHALLENGES for "Scream Train"
Complete all CHALLENGES for "The Fetid Waters"
Complete all CHALLENGES for "Jailhouse Judgment"
Complete all CHALLENGES for "Overkill"
Unlock all unlockables and purchase all weapons
Achieve an S rank for all levels in Story Mode or Director's Cut
Complete all levels in Classic Mode without using any continues
Complete all Director's Cut levels in Hardcore Mode