I think that the most obvious answer to this is that this action shows that the sniper is a ruthless man. He is willing to shoot even an old woman. To most of us, this would seem like an incomprehensible act because we are supposed to treat the old more gently than others. So his killing an old woman shows that he will do anything for his cause.
I think you can also say that he is a vengeful person. When he shoots her, she has already told the soldiers where he is. Killing her will not take that knowledge away from the soldiers. So his killing her shows that he wants to take revenge on people who try to hurt him.
So, overall, I'd say this shows him to be a ruthless and vengeful person at this point in the story.