Well, one of the challenges could be the manipulation by dark forces. Some fanfics might depict dark wizards trying to use the Tournament to harm Harry. They could try to rig the tasks against him. Another problem could be his own self - doubt. With so much pressure, he may start to question his abilities. And the tasks themselves may require new spells or skills that he has to quickly learn, like a particularly difficult form of magic for the second task in the lake.
There might be a fanfic where during the Triwizard Tournament, Harry gets cursed and Hermione has to find a way to break the curse. She races against time, using every spell and potion she knows. Meanwhile, she also has to deal with the tournament tasks on Harry's behalf. In the end, through her determination and love for Harry, she manages to break the curse and they both complete the tournament in an unexpected way.
His courage may become more pronounced. As he faces the dangerous tasks in the Tournament, he has to dig deeper into his bravery reserves. For example, if he has to face a more terrifying dragon, he'll have to be even bolder. His strategic thinking also improves. He has to plan how to approach each task, like figuring out the best way to get through the maze in the third task. And his sense of responsibility grows. Since he represents Hogwarts, he feels a greater obligation to succeed.
In a fanfic like this, there could be a lot of drama. For example, Pansy might be conflicted because of her Slytherin loyalty and her growing feelings for Harry. Harry, on the other hand, could be dealing with his own feelings while also trying to survive the dangerous tasks of the Triwizard Tournament. Their relationship could start with a lot of bickering and then slowly turn into something more romantic as they face the challenges together.
One possible scenario in this fanfiction could be that Harry and Fleur form an unexpected alliance during the Triwizard Tournament tasks. They might discover they have complementary skills, like Harry's courage and Fleur's elegance and magic related to water (since she's from Beauxbatons). This alliance could lead to them facing the challenges in a new and interesting way, perhaps with Fleur using her Veela charm in a creative manner to distract the obstacles while Harry uses his Gryffindor bravery to take on the more physical parts of the tasks.
One great fanfiction could be where Harry and Luna team up in a unique way during the Triwizard Tournament tasks. Maybe Luna uses her off - beat magical knowledge to help Harry solve the puzzles in the maze. For example, she might recognize some magical creatures that Harry is unfamiliar with and guide him through.
One possible fanfiction could be about Harry and Hermione teaming up secretly during the Triwizard Tournament tasks. They might use their combined knowledge and skills to outwit the other competitors. For example, in the maze task, they could have a special code to communicate and find their way to the Triwizard Cup faster than anyone else.
She could research about the dragons' species and their habits. By knowing what scares them or what attracts them, she can give Harry useful tips. For example, if she finds out that a certain type of music calms a particular dragon, Harry can use that during the task.
A plot could be that the Triwizard Tournament tasks are magically altered to target Harry specifically, and Hermione has to use her skills to figure out who is behind it. Maybe a new dark magic is involved that she has to research. She then has to train Harry in new ways to face the challenges. For example, teaching him some ancient spells that are not commonly known.
Another plot could revolve around a spell gone wrong during the Triwizard Tournament tasks. For example, the spell that creates the maze for the final task malfunctions and the maze becomes a living, sentient entity that changes and adapts to the champions' movements, making it much more difficult and dangerous to navigate.