This is another cumulative achievement, so you don't need to do it in all one play-through, which would be quite hard, since corruption increases sometime since you can't fight all missions.
For this, you want to focus on the missions that have a team size maximum of three.
Just put all 3 members on them and complete by fighting or deploying.
Since you are using all team members on this, you will only be able to play this mission on its day.
Good examples of missions that have the possibility of using three members are all omen missions, and the final one with Gargos. Those can not be deployed.
After you complete 10 of them, the achievement will unlock.