Here is the full list of all 13 CivIdle achievements.
The base game contains 12 achievements, and there is 1 DLC pack containing 1 achievements.
Reach Classical Age in any city (granted when you unlock any technology in that age)
Reach Iron Age in any city (granted when you unlock any technology in that age)
Reach Bronze Age in any city (granted when you unlock any technology in that age)
This special achievement is awarded to playertesters and players who played the game's demo
Rebirth with at least 1 Extra Great Person in Rome (Reach 64M Empire Value when rebirth)
Rebirth with at least 1 Extra Great Person in Athens (Reach 64M Empire Value when rebirth)
Reach Middle Age in any city (granted when you unlock any technology in that age)
Reach Renaissance Age in any city (granted when you unlock any technology in that age)
Reach Industrial Age in any city (granted when you unlock any technology in that age)
Rebirth with at least 1 Extra Great Person in Memphis (Reach 64M Empire Value when rebirth)
Reach World Wars Age in any city (granted when you unlock any technology in that age)
Rebirth with at least 1 Extra Great Person in Beijing (Reach 64M Empire Value when rebirth)
Reach Cold War Age in any city (granted when you unlock any technology in that age)