Once you have progressed far enough in the story, you will be able to fight warchiefs. Warchiefs are essentially stronger captains. They make up the fourth row in the "Sauron's Army" page. If you highlight the warchiefs, there will be a blue line showing which captains are their bodyguards. This means that if you go to fight this warchief, this (or these) captain(s) will be with him.
To earn this achievement, there are 2 options.
Option 1 - Take out his bodyguard(s) before you go to fight him, by getting intel on them and killing them.
or
Option 2 - I'm assuming I did it this way, since I just went straight after every warchief. You COULD just go straight after the warchief, and kill him and his bodyguards at the same time (killing bodyguards first obviously). This will obviously be a lot harder, and unless you're skilled at the combat at this game I wouldn't recommend it. Not to say it isn't doable, but depending on what combination of abilities they have it could be annoying.
(Example, I went after one and got killed when he had one bodyguard. I managed to beat him though when he had 2.)
I can't really confirm this option since I've already earned the achievement, so if anyone else could confirm it I'd appreciate it.
Another thing to add - I pretty much went around murdering every captain in the beginning of the game, so by the time warchiefs showed up, only like one had a guard. This leads me to believe that while you can't highlight the warchiefs in the beginning or see their links to the captains, the links are already there.