This achievement requires the player to play as the High Elves, and can only be obtained in the Eye of the Vortex campaign, as there are only two cities in the Mortal Empires campaign that can be upgraded to such a city (as of The Warden and the Paunch).
The four cities in question are (you only need three of the four):
Citadel of Dusk, in The Capes region (occupied by the Citadel of Dusk minor faction)
Great Turtle Isle, in the The Turtle Isles region
Tor Elasor in The Sea of Dread region (occupied by the Tor Elasor minor faction)
Fortress of Dawn in the Fortress of Dawn region (occupied by the Fortress of Dawn minor faction)
The two cities on the Mortal Empires map (as of yet) are:
Arnheim, The Black Coast (Alith Anar starting region)
The Star Tower, Volcanic Islands (Teclis starting region)
Both Eltharion's and Imrik's starting positions are not Thriving Elven Colonies. Eltharion's Gronti Mingol is an Elven colony but can only be upgraded to lvl 3, and Imrik's The Fortress of Vorag is not a colony.
You'll need to upgrade all three cities to a lvl 5 city. If you hover over the upgrade you'll see that it says "Thriving Elven Colony" and to the right of the name on the map it even has a special sign for it (same place as where strategic locations are marked).
When all three cities are lvl 5 (and under your control) your achievement should unlock.