Here is the full list of all 13 NecroCity Demo achievements.
Begin first mission
Complete first level
Complete second level
Complete third level
Complete fourth level
Fail at least one mission
Win without creation range units
Kill the peasant
Collect at least one chest
Build 50 buildings, exclude the traps
Create 50 units
Build 10 trapS
Spend one hour in the game event if it's paused