I would recommend you use http://dulfy.net/2014/07/30/gw2-the-dragons-reach-part-1-achievement-guide/ as a resource. In particular, there’s one inquest that will try to flee from you, and killing them prematurely will prohibit you from killing other asura, thereby failing the achievement (groups 10 and 11 in the dulfy guide).
Also note that you need to pick certain incorrect choices when dealing with the components you have to find.
I would double check that you are getting everything listed on the dulfy guide for leave no survivors. If you are, then I’m not sure why it wouldn’t be triggering.