Fortunately, rather hard to inflict. Sure, you can kill the body (corpicide) readily enough, with enough bullets or other regular weapons – get both hearts, or shred the brain, or pulverize the whole thing. But then the fun begins. First you need to get the vector stack where the immediate backup of their mind-state is stored (and hope that it didn’t come with an emergency bug-out transmitter, or it’s already too late). In a biological body, it’s somewhere near the base of the brain, but close enough to the surface to pull quickly in an emergency – in humanoids, the back of the neck is usual. Cut below it and yank. Then you’ve got to destroy that, which may itself require some exotic methods, since they’re designed to survive very large explosions up close, but is still possible.
So far, though, all you’ve done is given them some amnesia (unless they’re a Fusion or a synched cikrieth set of full-fidelity forks, in which case you need to go hunt down all their other instances, too. Actually, you probably want to go assassinate their utility forks anyway, on general principle), because they have a backup. In the absence of bug-out devices, it’s probably a few hours, maybe a day or two old, but at some point – quite likely right now, if they were on-line when you killed them – their incarnation insurer is going to stick said backup in a new body, and then they’ll be alive again.
So you have to crack their incarnation insurer’s security, physically or virtually, to destroy the backup copy of their mind-state. Actually, you’re going to have to do that quite a lot, since given the business that they’re in, incarnation insurers generally keep at least triple-triple redundant copies of people’s backups, including keeping older copies, and do so in physically isolated – scattered across multiple star systems – and heavily network-secured locations just to be sure.
But if you can manage that trick, you’re good. As long as they don’t have any backup backup copies stored in data havens, entrusted to friends, secured in hidden Oort bunkers on long-term proceed-unless-canceled wake-and-restore programs…
(And that’s even before we get to those strange folks who open-source themselves.)
Yes, permadeath is hard to arrange.
(This, incidentally, is another reason why the penalty for cognicide is so high – given all of this, in most cases it’s impossible to do without serious forward planning and therefore lots and lots of cold-blooded premeditation.)