Here is the full list of all 28 Hegemony III: Clash of the Ancients achievements.
Win a sandbox as a Sicilian faction
Win a sandbox as an Illyric faction
Win a sandbox as a Sabellic faction
Win a sandbox as a Gallic faction
Win a sandbox as a Greek faction
Proclaim Pyrrhus as King of Sicily by taking Eryx and Lilybaeum from Carthage
As Pyrrhus, protect Syracuse from Carthaginian invasion
As Pyrrhus, defeat the Roman army gathering at Asculum
Defeat Valerius Laevinus
Get the Tarentines to accept Pyrrhus' control of their city
Control every city of Sicily
Raze away 100 points of city population
Conquer all cities in the Unification sandbox
Maintain naval hegemony for 2 weeks
Defeat 1000 Brigades
Win a sandbox as a Latin faction
Raid 100 resource buildings from 0 to 100
Have a total population of at least 100 in a single game
Mine, tax or loot 100 000 gold
Defeat 500 Brigades
Maintain cultural hegmony for 2 weeks
Win a sandbox as an Etruscan faction
Maintain military hegemony for 2 weeks
Maintain trade hegemony for 2 weeks
Defeat 100 Brigades
Capture 1000 slaves
Harvest 100 000 000 food
Harvest 100 000 wood