Here is the full list of all 16 Empire Architect achievements.
Beat Level 3 of the "Glory of Rome" Campaign
Beat Level 2 of the "Glory of Rome" Campaign
Have a population of 100 or Higher.
Open a Trade Route.
Beat Level 1 of the "Glory of Rome" Campaign
Win a custom game.
Have a population of 200 or Higher
Have a population of 300 or Higher
Beat Level 4 of the "Glory of Rome" Campaign
Beat Level 5 of the "Glory of Rome" Campaign
Beat Level 6 of the "Glory of Rome" Campaign
Beat Virunum in the "Glory of Rome" campaign
Beat Sicilia in the "Glory of Rome" campaign
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Beat Cassel in the "Glory of Rome" campaign
Beat Faventia in the "Glory of Rome" campaign