The Harry Potter series is rife with mysterious lore that has yet to be fully explored. One bit of magic that still holds an aura of mystique are Horcruxes. Some of the darkest magic in all of the Wizarding World, Horcuxes require an individual to split their soul apart to transfer it to another object or living thing. To work, the magic requires the user to kill another person, a soul for a soul.
Very few wizards have attempted to produce a Horcrux. In canon, only two had successfully created one. The first to conjure said vessel was Herpo the Foul in Ancient Greece. Obviously, his was destroyed, as Herpo isn't running around causing trouble in a Toga. The second was obviously Voldemort, who unlike Herpo, created more than one Horcrux. Luckily, all of his were destroyed (by no easy feat). Destroying a Horcrux is an incredibly difficult task. As seen in the books and films, few objects or spells have the ability to eradicate a Horcrux thoroughly.
6 Living Versus Inanimate Horcruxes
One thing that needs to be understood is that a Horcrux can be made from any physical object or being. It does not matter whether it's a living creature or an insignificant trinket. This being the case, Voldemort made both inanimate objects and living creatures into his Horcruxes. Nagini, Harry, and arguably Professor Quirrell were all living beings carrying a piece of Voldemort's soul within them.
Unlike the physical objects such as Riddle's Diary, these creatures did not always need to be destroyed by something as powerful as say, the Sword of Griffyndor. Nothing more than the killing curse defeated the piece of Voldemort that lived within Harry. These logistics don't always work, as the killing curse was attempted on Nagini with no effect. The rules surrounding this loophole are not clear, but they are obviously present. That being said, let's look into every proven way a Horcrux can be destroyed.
First appearing in the novel Harry Potter and the Deathly Hallows, Fiendfyre is a piece of incredibly dark and dangerous magic. The conjurer of Firendfyre produces a bright and disastrous flame, often taking the form of beasts such as serpents, lions, and birds of prey. In the world of the films, Fiendfyre has appeared in The Order of the Phoenix during the duel between Dumbledore and Voldemort, and in The Half-Blood Prince when Bellatrix attacks the burrow.
This contradictory use of the magic also adds a wrinkle in its effectiveness against Horcruxes. In the book, when Fiendfyre chases the Trio in the Room of Requirement, they use the flames to destroy Ravenclaw's Diadem (one of Voldemort's Horcruxes). That being said, the film version showed Harry stabbing the diadem and Ron kicking it into the flames. So, the film world never fully confirms whether Fiendfyre is effective in destroying the Soul-filled vessel.
4 The Killing Curse
The killing curse is the most effective way to kill just about anything in the Harry Potter universe. Completely symptomless, the curse strips away the life from the body seamlessly. The killing curse does not seem to work against most Horcruxes, but once again, this gets into the weeds of distinction between film and book canon. The books do not present this scenario while the film directly shows the killing curse not working against Nagini.
Although it might not have killed Nagini, the killing curse did succeed in destroying the Horcrux side of Harry. Perhaps this is less a commentary on whether the curse works against Horcruxes as opposed to whether the curse works against magical snake/human hybrids. No matter what, the killing curse worked in destroying one Horcrux, giving it a permanent spot on this list.
3 The Sword of Gryffindor
As mentioned, the Sword of Gryffindor was a powerful weapon against Horcruxes. The sword itself held a mystical past. Forged by Goblin metalworkers, the sword is enchanted and would appear to a Gryffindor who was worthy and in dire need of it. Controversy regarding ownership whirled around the weapon, as the Goblin community believed it to be stolen. No matter the case, although it is a worthy piece of Hogwarts and Goblin history, it alone could not destroy a Horcrux.
The sword itself certainly had the potential, as Goblin metal absorbs that which makes it stronger. When Harry Potter used the sword to slay the Basilisk, it was imbued with the venom of the beast. This combination of ancient blade and powerful poison made the weapon a formidable tool in the search for Voldemort's treasures. Its added power allowed it to destroy any and all Horcruxes it encountered. Neville Longbottom used it to slay Nagini, Dumbledore used it to destroy the ring, and Ron did the same against the locket.
2 Basilisk Fang
It's starting to feel like all of these tools are connected. The most useful weapon against Horcruxes, seen so far, has been the venom of a Basilisk. Perhaps this elixir is closely tied to the dark nature of both Horcruxes and serpents. To fight terrible evil you must use terrible evil. Obviously, Voldemort was a Slytherin, but even the dark wizard Herpo the Foul had a pet Basilisk, ironically the same creature responsible for destroying most of Voldemort's Horcruxes.
The first moment the power of the Basilisk was revealed was in Harry Potter and the Chamber of Secrets. Harry used the fang to destroy, unbeknownst to him, the Horcrux that was Tom Riddle's diary. The venom would then go on to power the sword of Gryffindor as well as used to destroy Hufflepuff's Cup via fang. The Venom has been the Horcrux killing MVP since day one.
1 Sacrificial Love
A controversial point to be sure, but Quirrell easily could be considered a pseudo-Horcrux. He served as a vessel for Lord Voldemort's soul. Although the anatomy of this relationship was far different than say Harry or Nagini, there is no denying that the two were deeply connected in nearly the same level. Because of this, Quirrel might be seen as the first of Voldemort's Horcruxes to be destroyed.
But unlike most of these other vessels, Quirrell was destroyed not by the killing curse or a Basilisk's fang. Instead, it was the protective charm of love that defeated the duo. In The Sorcerer's Stone, merely the touch of Harry's hands cause Quirrell to crumble to dust. Obviously, this didn't work on traditional Horcruxes, but this moment is a hallmark moment in understanding the complexity and mystery of the Horcrux mythos.