For this achievement, you are required to complete 20 missions as part of a group.
Now for sure you can get this by playing through the main story missions, side missions, and the missions that appear as a yellow area with a yellow chevron after you complete the story missions (forget the name of these missions but there are three on the map, one that requires DLC). I'm not sure Security, Medical and Tech encounters count since I did all of those solo so if someone could let me know that would be sweet.
Anywho, if you want to join a group you can either do so at the various safehouses located throughout Manhattan (one per area), or you could go to the start of any story mission and search for groups for that specific mission. Simply complete 20 missions and voila, easy achievement.
Some personal experience from my playthrough of the game:
I played the entire game solo first. That way I could go through the missions and learn and absorb the story at my own pace. I completed the story missions, all the side missions and encounters and all the collectibles by myself, then started working towards the achievements for beating all the story missions on hard. This is where I started playing with groups of people for a few reasons:
-There are 16 story missions that you need to replay on Hard for
which knocks out 16/20 right there
-Odds are that one of those 16 times your team (unless you or them are incredibly bad), your entire team won't go down or die, earning you this achievement
-You need to complete one mission in Challenge difficulty which, believe me, you need a group for
giving you 17/20
Now for the last three I just played daily missions over and over again because you won't have to wait a while to find players to play with since there are always players on them.
Of course theres no need to follow my playstyle. If you prefer playing through the whole game with people thats perfectly fine too. But this is to show you theres no need to feel the need to have to unnecessarily grind this one out.
One thing to note, you DO NOT have to be in the group from mission start to mission end for them to count as completed. You could get lucky and join in right as the mission is about to end and get credit for it. This happened to me at the very last story mission. I joined in right at the end of the boss fight but before the mission was officially over and it counted for me. As for side missions/encounters I'm not too sure but I feel like it would be the same thing.