This is not a random achievement.
If you go in and select the first option (Charm) for the first sentinel you see, and it is the "right" one, then you can just continue to jump back in and back out on that same sentinel and get all 10 in the same run. Just continue to select the seemingly "random" options in order, charm then dignity, then ferocity. This works for whichever your "starting" guy is. If you get it wrong, jump out of the instance immediately and go back in. I've had the best luck with selecting charm on the first sentinel every time.
Not sure if anyone else has found it, but everything I've read keeps saying this is random, when its only random if you continue through trying to trigger different charr.