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