Inspired by this question
"You know Voldemort’s snake. Neville? He’s got a huge snake . . . Calls it Nagini . . .”
“I’ve heard, yeah . . . What about it?”
“It’s got to be killed. Ron and Hermione know that, but just in case they ---“ he pulled himself together again: This was crucial, he must be like Dumbledore, keep a cool head, make sure there were backups, others to carry on. Dumbledore had died knowing that three people still knew about the Horcruxes; now Neville would take Harry’s place: There would still be three in the secret.
“Just in case they’re --- busy --- and you get the chance ---“
“Kill the snake?”
“Kill the snake,” Harry repeated.
“All right, Harry. You’re okay, are you?”
Chapter 34, The Forest (Again)
Harry never specified how to kill the snake and (luckily) the sword of Griffindor presented itself to Neville when he needed it. I think we can assume that Neville isn't too aware of horcruxes and their weaknesses.
However, what would have happened if Neville had tried to kill Nagini in some other way (such as magic, a standard weapon) ?
(In addition, Voldermort seems to have killed one of the Horcruxes when he 'killed' Harry)
