I found the quickest way to get this achievement was to rinse and repeat Extra Ops Mission 035 - Hold Up. There are 7 guards in this mission that, once you know the route, takes about a minute to complete. Unfortunately, you cant hold up the 7 guards and restart the mission as the counter only seems to update when the game saves upon clearing a mission, so mission failures also are not counted. However, once you hit you're 100th, your chievo will pop mid-mission.
Also, having the Sneaking Uniform, you unlock this after the story mission with the attack chopper battle, helps tremendously as the guards won't hear you coming as it eliminates any sound you make whilst running. The button used to hold up a guard is different with each type of control configuration, but it's you're "aim weapon" button.
The first three, in the first area, are pretty easy to spot and require minimal effort to hold up. In the next area, there is a guard in the centre of the area, one patrolling the right side, one on the left side and one at the back up the stairs. The order I did these four was I did the centre guard, then the right side, then left side, then ran up the stairs to get the guard at the back.
You can check how many hold ups you have by going into the Player Data section in Mother Base Menu, then Profile, then go to the Mission Stats tab and it's the 6th statistic.