Here is the full list of all 41 Dead Nation: Apocalypse Edition trophies - there are 26 bronze, 10 silver, 4 gold and 1 platinum.
Survive to Round 5
Complete a Round with a Kills-per-minute rate of 100 or more
Collect All The Loot In Any Mission
Complete Mission 3 (Any Difficulty Level)
Complete Mission 2 (Any Difficulty Level)
Kill 1 000 Zombies
Fully Upgrade All Stats Of Any Weapon In Campaign Mode
Help Your Country To Clear The Virus Infection
Complete Mission 1 (Any Difficulty Level)
Complete A Mission Without Dying
Fully Upgrade A Single Stat Of Any Weapon In Campaign Mode
Collect An Armor Piece
Collect All Trophies
Complete Campaign Mode On 'Normal'
Complete Campaign Mode On 'Grim'
Complete Campaign Mode On 'Morbid'
Complete Campaign Mode In Co-Op Mode
Complete Mission 4 (Any Difficulty Level)
Complete Mission 5 (Any Difficulty Level)
Complete Mission 6 (Any Difficulty Level)
Complete Mission 7 (Any Difficulty Level)
Complete Mission 8 (Any Difficulty Level)
Complete Mission 9 (Any Difficulty Level)
Complete Mission 10 (Any Difficulty Level)
Complete A Mission In Co-Op Mode (Any Difficulty Level)
Complete A Mission On 'Undead'
Complete A Mission Without Receiving Any Damage
Kill 10 000 Zombies
Kill 53 597 Zombies
Perform 500 Headshots
Perform 500 Melee Kills
Blow Up 1 000 Zombies
Burn 1 000 Zombies
Destroy 500 Vehicles
Collect All Armor Pieces
Collect All The Loot In Every Mission
Find all mementos in single player campaign in a single playthrough
Survive to Round 10
Get the Apocalypse Combo Kill Bonus (150 Kills)
Complete a Round in Co-Op Without Either Player Taking Damage
Find all the Egogate emblems