Your selective reading fails once again. The first shot did not damage "essential centers in the CNS or upper cervical spinal cord" The bullet struck the posterior tubercle of the 4th vertebrae, that part does not cover the CNS.
Its a strawman argument to suggest the essential centers in the CNS were severed by the bullet anyway because that would have killed her instantly thus Jeremy would see no need to fire a second shot in the first place.
You're the one with selective reading
This is due to the fact that
immediate incapacitation occurs only if essential centers in the
CNS or upper cervical spinal cord are injured,
rapid
incapacitation occurring when hits produce massive bleeding
(heart, major vessels) - the bullet damaged her jugular!!