Here is the full list of all 30 Dead Purge: Outbreak achievements.
Kill 5000 zombies
Win 10 games
Reach level 5
Complete Suburb - Night level in Horde mode
Complete all levels in Horde mode
Complete Alley - Day level in Horde mode
Perform 1000 headshots
Complete Police Station level in Horde mode
Kill 1000 zombies
Perform 500 headshots
Complete Suburb - Sunset level in Horde mode
Complete Alley - Night level in Horde mode
Kill 500 zombies
Deal 100K damage
Complete Suburb - Day level in Horde mode
Win one game
Kill 250 zombies
Perform 150 headshots
Reach level 2
Kill 100 zombies
Perform 75 headshots
Kill 50 zombies
Deal 10K damage
Perform 25 headshots
Kill 10 zombies
Perform 5 headshots
Kill 10000 zombies
Win 100 games
Win 250 games
Reach level 10