YOU MUST BE ALIVE IN THE SAFE ROOM AT THE END OF EACH MISSION IF YOU WANT YOUR ACHIEVEMENT POP WHEN YOU FINISH THE ACT. If you die but your friends finish the mission, you will be able to continue the act. But at the end of this act, the achievement won't pop.
If so, just try again this mission online with at least one friend (bots do the job) and finish the mission alive in the safe room. If this mission is the only one you missed, the achievement will pop immediately for act.
This is the way a lot of players think the achievement is glitched. But it's not.