You get this achievement for liberating all districts in either Boston or New York. Boston can be liberated earlier as you can't travel to New York until after the missions for liberating Boston are available.
After meeting Stephane Chapeau during sequence six, the liberate Boston side missions will appear on your map. Once you have completed all these missions, you will be able to talk to your contact in the district, and you will start a mission to liberate this district. There are three districts, and the missions can be seen on the map (if you go to the fullscreen map in your menu, the option between the normal map and the hunting map shows you your progress).
There are a couple of different missions; some require you to liberate a prisoner, many have you kill guards (for a variety of reasons), but none should be really challenging. I advise you to use a horse to get to the missions in the south district, as some of them have an enemy on a horse that must be stopped. As stated in the comments, if you're alert enough it's easily possible to just shoot the guys off their horses - I mainly recommend a horse so that you can easily follow the guys if you miss or don't see them in time, plus you can travel across the fields a lot faster.
Once you liberate a district, your contact will turn into a recruit for the assassins.
The liberation of central Boston is part of the main storyline (sequence six, mission three: Angry Chef).
The liberation of south Boston requires you to kill a templar; you can do this quite easily by going clockwise around the forbidden area - just south of the target, you can climb the wall and get behind him, this way you can quickly assassinate him without having to fight through other enemies.
The liberation of north Boston requires you to kill a templar patrolling with some enemies. You can plow through them yourself, or call for aid of your new recruits.
Once you've liberated all three districts, the achievement unlocks.
The liberate Boston sidemissions will only appear on your map in places you've already discovered. If you're like me and you've already synchronised on top of all viewpoints, most missions should be visible already. If you notice you've done all visible missions in a district, but you don't get the 'liberate district' mission yet, you need to explore the unseen parts of your map. There is only one mission that didn't show directly on my map. This was a mission in the north district - on the top right side of north Boston (just left of the upper harbour master icon), there's a small forbidden area, in which my last remaining side mission was located. The area was only forbidden until I liberated the prisoner inside.
New York note:
I haven't liberated New York myself, but TillTheMorning noted that he couldn't complete the northern area. In the end, like the note above, this too was because of an easily missable part of the map. There's a mission on the far north-east part of the map, near the fort, that can be missed.
To negative voters, please explain your vote so I can improve on my solution.