Absent a half dozens shots in less than 2 seconds right through an eye socket into the brain, you'll get the hostage killed. You want to IMMEDIATELY KILL the perp to prevent his killing the hostage. Anything less will get the hostage killed.

Addendum: looking at your target, all the head shots but the one to the eye would likely bounce off the skull. The chance of any of the body shots resulting in an immediate incapacitation of the shooter is essentially zero. Even the (presumable) heart shot would do nothing because of the angle of the shot entering the body. There's very good reasons that .22 LR is not used by tactical teams for taking out perps.

And yea, except for for squirrel and rabbit hunting and rifle matches, the 15-22 IS just for plinking.