Here is the full list of all 36 Sniper Elite: Nazi Zombie Army 2 achievements.
Successfully complete Chapter 3 with 4 players
Defeat 500 enemies with headshots
Loot an Elite's corpse
Kill 1000 enemies
Pick up a phone
Kill any 100 enemy with the shotgun
Kill 500 enemy grunts
Defeat a Fire Demon
Become possessed
Get a 5-for-1 kill with any sniper rifle
Pick up a shotgun
Pick up the Preacher
Own 2 Nazi Zombie Army games
Kill 5000 enemies
Kill 20 enemies as they revive
Kill a suicide grunt by hitting his grenade
Kill 100 skeletons with explosives
Successfully complete Chapter 1 with 4 players
Successfully complete Chapter 2 with 4 players
Successfully complete Chapter 4 with 4 players
Successfully complete Chapter 5 with 4 players
Successfully complete All Chapters 4 players on Elite Difficulty
Get at least 10 for 1 explosive kill in 4 player co-op
Get at least 15 for 1 explosive kill in 4 player co-op
Get at least 20 for 1 explosive kill in 4 player co-op
Kick 50 enemies down in co-op
Kill 20 Snipers in co-op
Kill 2000 enemy grunts in co-op
Kill 20 Elites in co-op
Collect all Gold Bars
Find and shoot all the bottles of blood
Defeat 100 ignited zombies
Defeat 20 Summoners
Defeat 10 Fire Demons
Kill the trapped Elite
Defeat the Final Boss