The objectives for each mission are random, so the only thing you can do is keep completing the missions. Number of phases, directives or difficulty have no bearing on the mission objective.
Objectives include collecting reports, blowing up supplies, taking out a boss and so on.
There is no counter on the achievements app showing progress, so again, the only thing you can is play missions until it pops.
If it helps, I got this achievement after running a dozen missions, mostly hard, and was Underground Rank 9.