Since we don't know the specific 'hiccup girl story', it's impossible to say for sure who the main character is. But it's likely to be the girl who has the hiccups.
The 'hiccup girl story' could be about a girl who suddenly started hiccupping uncontrollably. Maybe it was a medical mystery at first. She might have visited various doctors, and they tried different treatments. It could also be a story of how her family and friends reacted to her situation, whether they were worried or tried to make her laugh to stop the hiccups. And perhaps in the end, she found an unexpected way to overcome this hiccup problem.
Astrid is likely to be one of the main characters to interact with Hiccup. She might be initially very confused or even a bit jealous depending on how she perceives Hiccup's new form. Stoick, Hiccup's father, would also have significant interactions. He would probably be shocked at first but then try to support his child in this strange situation. And of course, Toothless. Their bond is so strong that Toothless would surely be involved, perhaps trying to understand what has happened to his rider.
Another theme is often the alteration of her relationships. For instance, her relationship with her father might change as he might have different expectations of a daughter. Her friendships, especially with male characters, could also be different, perhaps more complex due to gender differences.
First, you need to establish the reason for the transformation. It could be a magical spell gone wrong, or some kind of strange dragon - related phenomenon. Then, focus on how Hiccup adjusts to her new body. She'll have to deal with different physical abilities and limitations. For example, she might be physically not as strong as before, but more agile in some ways.
A fanfic could explore how Hiccup's transformation into a girl affects his friendships. Astrid might react in a complex way. At first, she could be jealous or confused, but then they could form a stronger bond. Also, Hiccup's father, Stoick, might have a hard time adjusting to his son becoming a daughter, which could add a lot of emotional depth to the story.
One popular 'hiccup is a girl' fanfiction might be those that explore her relationships in a different way. For example, her friendship with other characters could be depicted in a more nuanced manner, like how she bonds with Astrid in a new light. Maybe she has different challenges and strengths as a girl compared to the original male Hiccup.
Well, one possible plot could be that Hiccup accidentally drinks a magic potion made by a mischievous wizard. As a girl, he (now she) has to deal with the different reactions of the people in Berk. Some are shocked, some are curious. And she has to learn how to adapt to the new body while still maintaining her heroic spirit, facing the same dragons but in a different physical form.
His relationships with others can also be a big part of his character development. If he meets other captives or his kidnappers, how he interacts with them, whether he tries to understand their motives or just fights back blindly, can show his growth. Maybe he starts off being angry and vengeful but then realizes that there's more to the situation and becomes more empathetic.
One interesting plot point could be how Hiccup adjusts to the new physical form. For example, he might struggle with the different clothing styles and social expectations for girls in his world. Another could be the reactions of his friends. Some might be shocked at first, while others could be more accepting and help him through the transition. There could also be a plot point about how this change affects his relationship with Toothless. Maybe Toothless initially doesn't recognize him and Hiccup has to find new ways to bond with his dragon.