Shooting
 

I want to film a scene where the impact of two bullets has to be shown on the person getting shot. I've seen some alternative pressure methods to making impact, but I don't want to use them. Any ideas out there, either from using on set techniques or after effects to make this blunt, as realistic, minimal but stark as possible.

For a wide shot, I'd attach a cord to the 'victims' body and pull it as he gets shot, that would make his body jerk backwards. Of course, you have to shoot him from an angle that hides the cord.
Are you referring to a close up shot of the impact site?
For a practical, you can use a hit of compressed air where the bullet hits, then overlay the spatter with AE. Slow-mo usually 'sells' the trick better.

Be very careful in using this technique, in fact on a non professional shoot, maybe don't use it at all. It is possible to damage someone's spine using this technique if you're not careful (sometimes it's possible even if you are careful).

There are particular techniques actors can use to portray the effect. Some acting teachers do specific workshops on stage fighting techniques (I've seen drama students learn to do staff that's totally same yet freakishly conbvincing, and I don't mean on camera, I mean actually acting it out in front of me). Such a teacher might feasibly know similar techniques for simulating gunshot impacts.

Safety first people.