Here is the full list of all 21 Age of Conquest IV achievements.
Win a game playing as Sparta.
Achievement for a completing the tutorial.
Achievement for a first game won.
Achievement for playing 1h or more.
Build a watch tower.
Hold a fertility festival in one of your settlements.
Eliminate 10 enemy units.
Achievement for playing 24h or more.
Achievement for 10 games won.
Win against the Inhuman-AI.
Eliminate 100 enemy units.
Eliminate 1000 enemy units.
Make a treaty with another culture.
Declare war against a much larger nation.
Hold 80% more of all the occupiable territory combined.
Being very liked by the AI players.
Being very much hated by the AI players.
Playing the first multiplayer game.
First multiplayer game won.
Creating a ballot to be voted on by others.
Casting a vote on a ballot.