Horcruxes can only be destroyed in specific circumstances that allow it's complete and utter destruction. In the movies, the horcruxes are destroyed in these ways: The killing curse — “Avada Kedavra.” Fiendfyre — a curse that creates powerful and magical flames.
We know for a fact that Basilisk venom is one of the few substances strong enough to destroy a Horcrux. Not only does it destroy the one inside Tom Riddle's diary, but Ron and Hermione also use one of the fangs to destroy Helga Hufflepuff's cup.
A Horcrux is considered destroyed when it's damaged beyond repair. In the case of living Horcruxes, “damaged beyond repair” would mean dead. So, yes, Avada Kedavra can destroy a Horcrux, as long as that Horcrux is a living being.
The Locket
Of all of Lord Voldemort's Horcruxes, Salazar Slytherin's old locket is the most difficult to obtain and destroy. In the Half Blood Prince, Harry Potter and Albus Dumbledore travel to an old cave where the Dark Lord would torture victims during his time as a teenager.
Expelliarmus did not beat Avada Kedavra.
Voldemort's wand (the elder wand) recognized its true master (that was Harry) and refused to attack it. In a way Voldemort killed himself as his own spell backfired on him.
And while many fan-favorite characters have fallen victim to the Killing Curse, one surprising figure working at Hogwarts School of Witchcraft and Wizardry may possess limited immunity from the spell's full, lethal effects: Rubeus Hagrid.
Quirrell is, in effect, turned into a temporary Horcrux by Voldemort. He is greatly depleted by the physical strain of fighting the far stronger, evil soul inside him.
Hermione Granger and Ron Weasley destroy the Hufflepuff's cup Horcrux inside the Chamber of Secrets—Hermione giving it the fatal blow with a basilisk fang.
Nagini was Lord Voldemort's final Horcrux
In an interview, J.K. Rowling revealed that it was the murder of Bertha Jorkins that made Nagini a Horcrux. After Voldemort discovered his Horcruxes were in danger, Nagini was magically protected, described as being encased in a 'starry, translucent sphere'.
Voldemort intentionally made six Horcruxes, but when he used Avada Kedavra on Harry, he unintentionally created a seventh Horcrux. Instead of dying, Lily's love for Harry created a counter 'curse' known as Sacrificial Protection and saved Harry.
In order to conjure the avada kedavra curse, you have to want to kill your victim. We all know that Voldemort could easily kill a child without an ounce of remorse... but not Snape. Snape didn't want to kill Dumbledore, and this was why the spell was blue instead of the usual green.
16. Avada Kedavra. J.K. Rowling has spoken about the root of this spell. According to Rowling, its root is actually Aramaic and derives from the original "abracadabra," which means "let the thing to be destroyed." In this case, the thing is a person.
Harry makes use of two of the Unforgivable Curses in the books. Dueling with Bellatrix Lestrange, he attempts the Cruciatus curse, with limited results; Bellatrix says that he has to really hate someone to make the Unforgivable Curses work properly, righteous indignation isn't enough.
Harry Potter became a Horcrux when the love from his mother protected him from Lord Voldemort's curse. Instead of killing Harry the curse backfired and destroyed Voldemort's body and all his power. In the course of this battle, Voldemort accidentally gave part of his powers to baby Harry as well as a piece of his soul.
The Dark Lord — aka Voldemort — created seven Horcruxes in an attempt to sustain immortality.
Neville played a significant part in the two final books and the fight against Lord Voldemort, destroying the final Horcrux, Nagini, with the Sword of Gryffindor.
Analysis. It is perhaps interesting that no person destroyed more than one Horcrux. Harry, Ron, Hermione, Neville, Dumbledore, Crabbe (indirectly: the diadem fell apart in Harry's hands after being damaged by Crabbe's fiendfyre), and Voldemort each destroyed one of the seven.
Each time a Horcrux was destroyed, Voldemort got weaker. The Golden Trio set about on a Horcrux hunt during Harry Potter and The Deathly Hallows, but they had already destroyed two by the time they embarked on their harrowing journey.
Salazar Slytherin's locket
Eventually it made its way to Hepzibah Smith's collection. After robbing Hepzibah, Voldemort made another Horcrux by killing a homeless Muggle, then hid the locket in a remote cave protected by Dark magic and Inferi.
She was sorted into Slytherin House at Hogwarts School of Witchcraft and Wizardry and hated her time at the school due to never being given any positions of power. After her time at Hogwarts, Umbridge rose to prominent and influential positions in the Ministry of Magic in the Improper Use of Magic Office.
At the time Harry touched him, Quirrell was sharing a body with Voldemort. Since the magical blood protection Harry had prevented Voldemort from touching him, Quirrell would suffer pain. He would ultimately be destroyed from touching Harry.
Albus Percival Wulfric Brian Dumbledore was the only wizard Voldemort ever feared and the only one who could have defeated him in a duel. Albus Dumbledore is the most powerful wizard in the Harry Potter.
In the opening scene of The Secrets of Dumbledore, Albus Dumbledore (Jude Law) revealed that he was in fact in love with Gellert Grindelwald (Mads Mikkelsen) when they were teenagers, and the blood oath was a witness of their love.