Here is the full list of all 26 Sniper Elite: Nazi Zombie Army achievements.
Kill 20 Elites in co-op
Kill 5000 enemies
Kill 100 skeletons with explosives
Successfully complete Chapter 5 with 4 players
Successfully complete All Chapters 4 players on Elite Difficulty
Kill the Occult General
Successfully complete Chapter 1 with 4 players
Own 2 Nazi Zombie Army games
Collect all Gold Bars
Find and shoot all the bottles of blood
Kill a suicide grunt by hitting his grenade
Kill 2000 enemy grunts in co-op
Kill 20 Snipers in co-op
Kill any 100 enemy with the shotgun
Kill 20 enemies as they revive
Kick 50 enemies down in co-op
Successfully complete Chapter 4 with 4 players
Kill 1000 enemies
Successfully complete Chapter 3 with 4 players
Successfully complete Chapter 2 with 4 players
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
Kill 500 enemy grunts
Pick up the Preacher
Pick up a shotgun