General tips[]
In fights, the real psy-dog tends to run around a little ways out from where the player is. Thus, players can sometimes benefit from ignoring the dogs in the immediate vicinity and instead looking for a lone dog somewhere close by. However, the dogs seem tangible, as one cannot simply move over them and their attacks, though futile, still stagger the player, preventing him from effectively falling back.
Combat Tips[]
The best way to kill a Psy Dog is to keep tabs on every image it makes and see if it is either a newly created image or if it might be the real one. All images disappear after being shot by any weapon, even by a single pellet of a shotgun's shot shell, and since the images immediately disappear the only one that bleeds is the real thing. Another way of killing a Psy Dog is leading it to an anomaly field and let the Zone's horrors ironically kill one of its own. Keep in mind that the Psy Dog does not immediately attack the player after sending its images and will usually stay out of sight of the player until the time is right. Normally the red dot on the map is the real psy-dog. Find it, and kill it and the rest will disappear.