The answer is: Barry is incorrect because his use of force was not necessary to prevent death or great bodily harm to himself or another or to prevent the imminent commission of a felony.
The key to this case is the time when Barry chose to shot the robbers. If Barry chose the robber while the robber is in his close proximity and turn his attention toward Barry, the shot could be justified as self-defense.
But in this situation, Barry made the shot after the robber fled and no longer cause a life threat for Barry. Because of this, we can make the argument that the force is no longer necessary.