For those wondering, unlike the "Party People" achievement, this achievement DOES NOT require you to complete the campaign in 4 player coop. It can be done with 2, 3 or 4 players on any difficulty.
So, simply complete the Judgement campaign in coop (not Aftermath) with at least 1 other person, and this one will pop
.
20-Apr-13 EDIT:From the comments, "umainbearman" and "TheHurt1974" confirm that this achievement can be done split-screen.
24-Apr-13 EDIT:If you have not got the achievement and wish to check if you have completed all chapters and sections on coop, then there is a way to check:
From the main menu, go to campaign and then Judgement/Aftermath, and then "Select Chapter". It will then ask you for a save location (1 of the 3).
Next, each "Testimony" is broken down into several chapters.
The "Testimony" will have a coop icon in the bottom right corner showing 2 white player icons if it has been completed
(the difficulty is also shown in the top right).
If 1 of those white-icons is missing, you can enter that testimony and check each individual section to see which 1 has the icon missing. You can then simply load that section and complete it.
Note that I've completed the game on 3player coop, but it only shows 2 player icons for all sections, unlike Gears 3 which showed 3 icons for the 3 players, and 4 icons for 4 players.
You can also check the "Campaign Leaderboards" under the Stats/Awards screen, but your campaign scores will only be tracked and logged if your Party type is set to "Joinable Friends" or "Joinable Public".