It could be an entirely new type of dragon created specifically for this fanfiction. The author might have wanted to introduce a unique dragon with special abilities, like a dragon that can change its color to blend in with its surroundings or one that can breathe not just fire but also some kind of magical ice. Harry would then have an even greater challenge when trying to kill it with the sword.
In many Harry Potter - related stories, the sword of Gryffindor often finds its way to those who are worthy. Maybe in this fanfiction, Harry discovers it in a similar way. It could be hidden in the Sorting Hat, or perhaps it's presented to him by some magical creature that recognizes his need and his courage.
In certain 'Harry kills the dragon' fanfictions, Harry could be given a special magical weapon specifically designed to slay dragons. He might have to go through a series of trials to figure out how to use this weapon effectively. It could be that the weapon has to be powered by his own magic and emotions. Once he masters this, he is able to take on the dragon and kill it. For example, the weapon might need to be charged with his feelings of courage and determination, which are strong in Harry, and then he uses it to strike a fatal blow to the dragon.
In many fanfictions, Harry might use his powerful spells like the Stunning Spell or the Killing Curse if the story allows for such dark magic use. He could also use his intelligence to outwit the dragon, perhaps finding a weakness in its armor or behavior pattern and then using a well - timed spell to defeat it.
Often, in these fanfictions, Harry's knowledge of the Horntail's weaknesses plays a crucial role. He might have spent time researching about the Horntail in the library at Hogwarts. When it comes to the actual fight, he uses this knowledge. He aims for the Horntail's soft underbelly or its eyes, areas that are more vulnerable, and with a well - aimed spell or a thrust of a weapon, he kills the Horntail.
The dragon sword might give Harry Potter enhanced combat abilities. It could potentially allow him to cut through dark magic defenses more easily, much like how the Sword of Gryffindor could destroy Horcruxes. Maybe it gives him the power to communicate with dragons, since it's a dragon sword, and use their strength in battles against Voldemort and his Death Eaters.
One consequence could be that he becomes a hero among his peers. Everyone in Hogwarts might look up to him even more. The other students could see him as a real dragon - slayer, which gives him more popularity and respect.
It could be in a fanfic where Harry teams up with someone powerful or uses a clever strategy that no one expected. The story could also change the nature of the task or the dragon itself to make it possible for Harry to succeed early on.
Well, it could be a magical sword like the Sword of Gryffindor. In many fanfics, authors might choose this iconic sword as it has a strong connection to Harry through Gryffindor. It's a powerful weapon against dark magic and has a lot of history within the Harry Potter universe.
There's also a possibility that it's a Chinese Fireball. These dragons are very beautiful and powerful. In a fanfiction, the author might choose this type of dragon for Harry Potter to own because it would add an element of exoticism and grandeur to the story.
He may use a powerful spell combination. For example, he could start with a Confundus Charm to confuse the Horntail and then follow up with a blasting spell to deal a significant amount of damage.