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