Yes..he was trying to avoid killing him.
So there were 4 shots in the arm before the 2 shots to the head that killed him? And one of the shots to his head went in his eye, through his face, and came back in at the jaw, and the other went into the top of his head indicating that his head was down?
If so, then it seems like 4 of the shots might have been to stop him and the head shots were fired when it was clear he wasn’t going to stop.