To earn this achievement you must be playing as Hurk when you liberate an outpost in co-op. You play as Hurk by default if you join anyone else's co-op game.
This can be a friend that starts a Friends Only session or by searching for an open session with a random in the Co-op menu.
You will not earn this achievement if you are the host of the co-op session (by inviting someone to join you they take the role of Hurk while you remain as Ajay).
It can be completed on any level outpost too (easy, medium or hard). Once the last kill has been done and the confirmation comes up on the screen that the outpost has been liberated; you will earn the Brother In Arms achievement.
In response to the comment by Su1c1deman; please note that the Outpost Master, which allows you to replay outposts you have already liberated, is not available in Co-op.
As of 17th Feb this has been proved to be untrue; thank you to Scubbasteve223 for stating that, following a patch to the game, the Outpost Master is now available in co-op. It is the host who must initiate this and the achievement unlocks upon completion of the selected outpost. Thanks also to The Ulkesh for confirming.
EDIT: Thanks to XboxFreak36 for confirming that you can also earn this achievement by liberating a Fortress.
Thanks also to samsaBEAR who has noted that if you want to help out a fellow player with this achievement and you have already liberated all the outposts, that you can reset your outposts in the options menu to allow them to unlock it. Always nice to help others out! ;)