If you wanted too after you killed a demon you can just reload last checkpoint and kill it again it will grant you the achievement and is the easier way to do it.
A good method to kill the demon is to wait until it gets close , and use the shotgun to shoot it , after it has circled around you a few times and you have taken a few bullets into it , it will eventually die.
This can be done after you broadcast the message on top of the building on the OUTPOST mission e.g (DJ Artyom achievement)
There will be a demon on the roof circling it and flying about , take cover in the little shack thing that you broadcast the message on and each time the demon gets close , shoot it :)
And can also be done on the TOWER mission where Miller gets attacked by a demon.
Hope this has helped and good luck.