Really bad idea...
The biggest thing you should think about, if you are really justified in shooting at someone, chances are the bad guy is loaded up on chemicals, drugs and alcohol for starters, and he may be so high he vibrates... stationary head... ??? b). Not likely he/she/it will be alone... As suggested "waiting" will get you killed...
At the same time, you will be "high" on adrenalin unless you are high on martinis and downers or uppers legally, not likely... You may "piss your pants"/ vomit/ shake uncontrollably... try to find a "combat veteran" who will discuss it... they don't want to remember unless they are NUTS... or so the few I have known have told me... (and then there are the nightmares... cf Audie Murphy's biography, not in the movie "To Hell and Back", gee why...) There is a reason they say "save the last one for yourself" they don't wish to discuss.
Number ONE is always "take cover" unless there is absolutely no time at all, then you shove the gun in the guys mouth and fire... hey a head shot...
Much better a bag of cell phones with 911 on speed dial. Hide and call 911 repeatedly, don't talk, dial another phone. 911 will be unhappy but they will send the troops. Let them do the shooting and clean up...
Number TWO is "aim for center of mass" and shoot more than once 'CAUSE you may not hit... I do NOT care what your score on paper is...
Number Three, as suggested, the effects on a skull by a bullet at close range is very unpredictable... Serpico, as I recall, had a .22 target pistol on his temple when fired. Bullet went down the bone to his ear and messed it up. Can't hear good one ear but went on breathing. NYC cop told, in video, of a shoot out, bad guy had a .45 ACP, cops had just encased shotguns and drew two snubbies by mistake--it happens. One 5 shot and one 6. Bad guy walked between them, gun on store owner, both cops opened up... 11 shots to the head. Bad guy went down, dropped gun. They called in. When the ambulance arrived someone said, "Ambulance is here" and the bad guy got up and walked to the ambulance !!!
Pray it never happens. Pray sincerely and often. If it does and taking cover is not possible shoot repeatedly for center of mass and hope you hit something... and don't forget the other bad guys... luck.