In The Deathly Hallows Hermione says this about destroying Horcruxes:
“It doesn’t have to be a basilisk fang,” said Hermione patiently. “It has to be something so destructive that the Horcrux can’t repair itself. Basilisk venom only has one antidote, and it’s incredibly rare—"
"That’s a problem we’re going to have to solve though, because ripping, smashing, or crushing a Horcrux won’t do the trick. You’ve got to put it beyond magical repair.”
Mad-Eye Moody from The Goblet of Fire tells us this about Avada Kedavra,
...there's no countercurse. There's no blocking it.
but also that,
Avada Kedavra's a curse that needs a powerful bit of magic behind it - you could all get your wands out now and point them at me and say the words, and I doubt I'd get so much as a nosebleed.
Harry is also seen once attempting to use Crucio on Bellatrix Lestrange in The Order of the Phoenix out of anger at the death of Sirius, but he fails. She tells him,
"You need to mean [Unforgivable Curses], Potter! You need to really want to cause pain - to enjoy it - righteous anger won't hurt me for long - I'll show you how it is done, shall I? I'll give you a lesson -"
Even if Harry and company are not powerful enough to perform the curse themselves, they know several powerful wizards (Kingsley, Lupin, et al.) who could likely perform the curse.
Lastly we know that Voldemort himself destroyed the last bit of his soul that was inside Harry with Avada Kedavra.
Could the Horcruxes be destroyed with Avada Kedavra as well?