To own a control point you need to position your Rally Troop over one of them. Your troops will then follow and when they reach the rally point that your Rally Troop is standing on, they will sacrifice themselves which will begin the takeover of the rally point. After enough time and sacrifice the rally point will be yours.
To unlock this achievement you need to be in a 4-player game and have control of all 4 of the rally points at the same time. You can try for this through playing the campaign, which would be rather difficult or you can set up a local 4-player game, provided you have 4 controllers and have your profile take over the 4 rally points, making for a quick and painless achievement.