This is unlocked in DNA sequence 3.
You can find the mediterranean defense game on the maps in your assassin dens (on the table under the stairs), HQ (on a table in the large main room) or also by using pigeon coops (which can be found by bomb crafting tables on the map) once you start recruiting your assassins.
There are 12 cities in total that you need to claim for the assassins (excluding Rhodes, for whatever reason).
***EDIT - Rhodes is unlocked when a match on each multiplayer map set in the city is played. The maps are Knight's Hospital, Souk and Ippokratous.
(Thanks to Hitman881103 & bbgmp for pointing this out, double-checked on AC wiki)
Best to do once your assassins are trained up a few levels or if you have a bunch of them for better odds of success. The game is similar to the one in Brotherhood in that you send your assassins on missions to collect money, experience points and items. This time, however, you can steal cities from the Templars.
Simply go in to the game, pick a city that you need, and then select reclaim the city. These missions take a little longer, so you'll need to be patient.
Also note that the templars will attempt to take back the cities after a time. The city will then be under siege and you'll need to protect it. Just choose the city being attacked and then the option to defend the city. Just like capturing it the first time, it will require either a bunch of medium ranked assassins or a couple highly ranked assassins to make sure the odds are in your favour.
Once the 12 cities are under your control the achievement will pop.
***EDIT - Thanks to Obi TW0, who brought up a really good point in the comments.
"Even then the percentage goes down though. I only realised for the first time last night that once you've assigned assassins to a city, they can still actually do missions within that city, meaning you can have missions underway constantly in every city you control. For ages I've been sending out my normal recruits to these without realising!
Once you choose a mission, press "X" to switch to the assassins that are in that city to allocate them to the mission instead. You can also mix and match between city assassins and your regular ones."