With Arya Stark, Achilles could be a mentor - like figure. Arya is on her journey to become a great fighter, and Achilles, with all his battle experience, could teach her new techniques and a different perspective on combat. However, their cultural differences, Achilles from Greek mythology and Arya from Westeros, could also create some interesting clashes and learning opportunities for both characters.
Aragorn's character arc could involve him initially being a reluctant participant in Westeros' affairs. But as he discovers the true nature of the threats like the dragons or the White Walkers, he transforms into a more active and determined figure. He could go from being a lone wolf to a leader who unites different factions against a common enemy. Along the way, he might also have to deal with his own inner demons and the differences in culture between his homeland and Westeros.
The Hulk would probably have a very different dynamic with the various characters. With the more honorable characters like Ned Stark, they might initially be cautious but then try to reason with the Hulk or at least figure out how to co - exist with him. However, with more power - hungry characters like Cersei, she might see the Hulk as a threat to her rule and try to eliminate him.
One possible character arc for Merlin could be that he starts as an outsider, just like in his original story. He comes to Westeros and has to learn about the different cultures and politics here. As he gets more involved, he realizes the importance of using his magic for good in this new and dangerous world. He might start by helping the smallfolk, and then gradually get involved in the bigger power struggles, all the while maintaining his sense of right and wrong.
She could be a maester - like figure. With her vast knowledge, she could advise rulers on various matters, from war strategies (using her strategic thinking from Hogwarts battles) to matters of health and economy. She'd be different from the traditional maesters as she has a more modern - thinking approach.
She could be a powerful sorceress. In the world of Game of Thrones, magic is a mysterious and dangerous force. Bella might be someone who has been secretly studying magic, perhaps in the far reaches of Essos. She could use her powers to manipulate the political situation in Westeros, for example, by influencing the minds of the lords and ladies during their councils. This would add a new and interesting dynamic to the complex web of power struggles in the series.
She could start as an outsider, just like Harry in the original story. But in the Game of Thrones world, she'd have to quickly learn the ways of Westeros. Her arc might involve her gradually becoming a key player in the power struggles, starting from a position of weakness and rising to a position of influence.
He could have an adventure where he goes on a quest to find a magical weapon. This weapon could be a Valyrian steel sword that was lost during the Blackfyre Rebellions. The search for it takes him to dangerous places like the ruins of Valyria or the dark forests of the North.
In a fanfiction, Wolverine could have a complex relationship with the villains. Some villains might be afraid of him because of his reputation and power. But there could be a villain who tries to manipulate Wolverine's past traumas. This could lead to some intense emotional and physical battles, as Wolverine has to fight not only the villain's powers but also his own inner demons.
A plot could center around a female mercenary who disguises herself as a man to join a group of male mercenaries. They are hired to fight in a civil war between two rival houses. As the war progresses, she falls in love with one of the soldiers on the opposing side. She has to balance her feelings, her identity as a mercenary, and the loyalty she owes to her comrades while trying to find a way to end the war without sacrificing too many lives.
Hashirama might become a powerful ally or a feared enemy in the Game of Thrones fanfiction. If he aligns himself with a certain house, his powers would make that house very difficult to defeat. He could also be a lone wanderer, using his skills to help the common folk. For instance, he could use his wood - style jutsu to create shelters for the poor or to clear paths in the forest for travelers. He would be like a force of nature in the world of Westeros, disrupting the normal power dynamics.