Here is the full list of all 64 Zombie Army Trilogy trophies - there are 60 bronze, 2 silver, 1 gold and 1 platinum.
Kill 50 enemies that are actively attacking other players
Successfully complete Freight Train of Fear
Get an unbroken 10-headshot streak
Reach a Chain Count of 30
Successfully complete City of Ashes
Kill a Survivor
Successfully complete Tower of Hellfire
Get at least 15 for 1 with an explosive kill
Successfully complete Terminal
Kill 20 Elites in co-op
Kill 50 Suicide Zombies
Successfully complete Crucible of Evil
Kill a Zombie Sniper in mid-air
Kill 20 enemies as they revive
Headshot a Heavy Armour Zombie without removing his helmet
Kill a total of 20 enemies while incapacitated
Successfully complete Gateway to Hell
Successfully complete Purgatory
Successfully complete Subway to Hell
Defeat 500 enemies with headshots
Successfully complete Library of Evil
Sever 1,000 limbs
Successfully complete Labyrinth of Death
Loot a Super Elite's corpse
Successfully complete Cathedral of Resurrection
Kill an Occult General
Pick up a Panzerfaust
Reach a Chain Count of 20
Successfully complete Village of the Dead
Pick up the Preacher
Get at least 10 for 1 with an explosive kill
Kill a Suicide Zombie by hitting his grenade
Kick 50 enemies down
Reach a Chain Count of 10
Platinum Trophy
Successfully complete Forest of Corpses
Successfully complete The Keep
Successfully complete Army of Darkness
Successfully complete all Chapters on Sniper Elite difficulty
Kill 5000 enemies of any kind
Kill 500 Skeletons
Kill 100 Zombie Snipers
Kill 50 Super Elites
Kill 25 Fire Demons
Kill 25 Summoners
Get a 5-for-1 kill with any sniper rifle
Reach a total shot distance of 50km
Sever 10,000 limbs
Loot a Chainsaw Elite's corpse
Get at least 20 for 1 with an explosive kill
Score 5,000 with a single sniper round
Reach at least Wave 10 in Horde Mode – Waves of Despair
Reach at least Wave 10 in Horde Mode – No Sanctuary
Reach at least Wave 10 in Horde Mode – Flood of Tears
Reach at least Wave 10 with the highest score in any Horde Mode map
Reach at least Wave 10 with more gold medals than your companions
Revive other players 50 times
Complete any Campaign chapter in 4-player co-op at any difficulty level
Complete every Survivor sidequest
Complete levels as every playable character
Collect every Gold Bar
Find and shoot every Bottle of Blood
Reach at least Wave 10 in Horde Mode – Dead End
Reach at least Wave 10 in Horde Mode – Dead Man's Bluff