Here is the full list of all 68 Zombie Army Trilogy achievements. It takes around 30-35 hours to unlock all of the achievements on Windows.
Get an unbroken 10-headshot streak
Successfully complete Gateway to Hell
Kill 50 enemies that are actively attacking other players
Successfully complete Purgatory
Successfully complete Subway to Hell
Get at least 20 for 1 with an explosive kill
Reach a Chain Count of 20
Get at least 15 for 1 with an explosive kill
Successfully complete Library of Evil
Sever 1,000 limbs
Successfully complete Labyrinth of Death
Defeat 500 enemies with headshots
Headshot a Heavy Armour Zombie without removing his helmet
Successfully complete Cathedral of Resurrection
Get at least 10 for 1 with an explosive kill
Get a 5-for-1 kill with any sniper rifle
Kill a total of 20 enemies while incapacitated
Kick 50 enemies down
Successfully complete Village of the Dead
Complete any Campaign chapter in 4-player co-op at any difficulty level
Kill 20 enemies as they revive
Kill a Zombie Sniper in mid-air
Pick up a Panzerfaust
Pick up the Preacher
Reach a Chain Count of 10
Successfully complete Crucible of Evil
Successfully complete Terminal
Successfully complete Tower of Hellfire
Successfully complete City of Ashes
Successfully complete Freight Train of Fear
Successfully complete Forest of Corpses
Successfully complete The Keep
Successfully complete Army of Darkness
Successfully complete all Chapters on Sniper Elite difficulty
Kill 5,000 enemies of any kind
Kill 500 Skeletons
Kill 100 Zombie Snipers
Kill 50 Suicide Zombies
Kill 50 Super Elites
Kill 25 Fire Demons
Kill 25 Summoners
Kill an Occult General
Reach a total shot distance of 50km
Sever 10,000 limbs
Loot a Super Elite's corpse
Loot a Chainsaw Elite's corpse
Kill a Suicide Zombie by hitting his grenade
Score 5,000 with a single sniper round
Reach a Chain Count of 30
Become possessed
Pick up a phone
Save the man in the hospital
Put the tortured souls in the Forest out of their misery
Shoot the 3 Zombie Ravens outside the Folterschloss
Reach at least Wave 10 in Horde Mode – Waves of Despair
Reach at least Wave 10 in Horde Mode – Cathedral
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
Kill 20 Elites in co-op
Complete every Survivor sidequest
Kill a Survivor
Complete levels as every playable character
Collect every Gold Bar
Find and shoot every Bottle of Blood
Reach Wave 10 in Horde Mode – Dead End
Reach Wave 10 in Horde Mode – Dead Man's Bluff