If you haven't unlocked this achievement before you get your companions, You might struggle more than the necessary on higher missions, Cause your companions don't rest and they are pretty capable to kill the boss in the S rank time frame. (if they are strong enough).
So, If you are starting the game, or you chose to restart the game, you have to get this achievement before completing the D-missions.:
(If you already completed the 10 B missions, and everybody at level 20, you might only be missing this achievement) .
First choose a character that you feel comfortable with, for example Sean or Shaw (The guy).
Then you will have only at the moment the Lava Guardian Mission available. So we will go into it.
At the start of the level manage to reduce his HP to at least 30-40%. Once is done free roam dodging him until your timer reach the 2 minutes remaining. At that point you need to kill the boss.
So if you manage to stand 3 minutes with him, you will have an A ranking (more easy than trying to beat a class B boss with your annoying partners, if you ask me)
Just repeat 4 more times to unlock the achievement (if you already have some A ranks victories, they will not reset if you delete your file).