Here is the full list of all 28 Dead Horde achievements.
Kill 10000 mutants
Died 50x
Kill 5000 mutants
Finish the campaign in Insane
Finish the campaign in Hard
Died 10x
Finish one mission in difficulty hard without being killed
Finish the campaign in Normal
Finish the campaign in Easy
Finish the map Junk Yard
Finish the map Military Base
Purchase all weapons in the campaign
Finish the map Highway
Pickup 21 money packs
Kill 1000 mutants
Finish the map Airport
Purchase all grenade types in the campaign
Finish the map Town
Finish the map Harbor
Upgrade the assault rifle to the max in the campaign
Finish a mission in less than 12 minutes
Finish the map Village
Finish the map Depot
Bonus multiplier reached 100
Finish the map Factory
Bonus multiplier reached 50
Bonus multiplier reached 10
Kill 10 mutants