For this achievement, you need to complete all chapters of any act in 3 player co-op.
It doesn't matter who you play as, but you might as well try to stack it with the Jack of One Trade achievement.
Upon unlocking this achievement myself, I learned that it is not necessary to do it all in the same run, nor even with the same people!
I tried getting this achievement with randoms, joining random people that were playing act 1.
I got chapter 1 and 4 done in one day, chapter 2 with other people in another, and finally chapter 3 today, unlocking the achievement.
There is a lot of misinformation regarding this achievement so I figured I'd throw my two cents in.