Here is the full list of all 20 Imperi achievements.
Reach rank of Officer
Reach rank of Lieutenant
Lose residents to famine
Lose residents to disease
Reach rank of Captain
Reach rank of Major
Reach rank of Colonel
Reach rank of General
Reach rank of Commander
Reach rank of Magistrate
Reach rank of Governor
Reach rank of Province King
Tax residents until some leave
Lose troops to desertion
Win territory in battle
Acquire 10,000 grain
Acquire 1,200 territory
Acquire 2,500 troop army
Acquire 5,000 treasury
Have a bountiful harvest