Your adrenaline may be shooting through the roof. Your not going to be as good as you are at the range shooting at paper targets. If you shoot at him you will likely cause him great fear as well though. Perhaps the only thing behind your gun will be your hand and air. I have seen war footage were combatants would hold their ak's with one hand out shooting and keeping their body behind a wall.
Seen the same sort of shooting from behind a wall done by U S troops during the Tet Offensive. This being to draw fire away from troops try to flank the enemy and hopefully keep their heads down.
Not a very useful tactic in a one on one fight with limited ammunition, but as you say it might break his self image of invincibility and send him scurrying for cover, and might distract him long enough for others to escape.