A strong plot. It should have a plot that goes beyond the obvious. Instead of just retelling what happened in the show or the books, it could take an alternative path. Maybe it could explore what would have happened if Robb had made different decisions during the War of the Five Kings. This kind of plot exploration requires intelligence and creativity from the writer.
You can start by looking on fanfiction websites like Archive of Our Own (AO3). There are often many talented writers who create intelligent and engaging Robb Stark fanfictions on that platform. Just use the search function and type in 'Robb Stark' to browse through the available stories.
One consequence could be a shift in the power balance. The Mountain was a powerful fighter in service of certain lords. His death would leave a power vacuum among his allies. Robb Stark, on the other hand, would gain more notoriety. His reputation as a fearsome and capable leader would spread, making his enemies more cautious of him.
Well, in the fanfiction world, Robb Stark might also get some unexpected help. Maybe there are some magical elements involved. A wizard or a sorceress could weaken the Mountain's strength or defenses. This would give Robb an edge in the fight. Then, with his courage and fighting skills, he could step in and slay the Mountain.
The Old Gods themselves would be crucial. They could be represented in various forms like the weirwood trees. And there might be some sort of priest or seer who serves as an intermediary between Robb and the Old Gods, guiding him through the spiritual experiences.
There's a fanfic titled 'Robb Stark's Sister: A Tale with Theon'. In this one, the female Robb Stark character is really strong - willed. She has her own ideas about the future of Winterfell and her relationship with Theon is full of twists and turns. The author does a great job of showing how their different backgrounds shape their interactions. It's an interesting read if you like character - driven stories.
A sense of adventure is also present. They were in the middle of a war - torn Westeros. Fanfictions might take them on different adventures together, away from the main battles, or they could be involved in secret missions that test their relationship. Also, the theme of loyalty, both to each other and to their respective causes, is explored. How they balance their loyalty to each other with their loyalty to their families and kingdoms is a rich area for fanfiction writers.
I recommend 'Robb Stark: The Lost Legacy'. This fanfiction focuses on an alternate timeline where Robb survives. It's interesting as it explores how he would have changed the course of the story. It has some great character development and interactions with other key characters from the series.
There's a fanfiction called 'Fem Jon Snow's Adventure with Robb Stark'. It's a detailed story that begins with their childhood. The author has beautifully described their personalities as females. For example, fem Jon Snow is brave yet has a more delicate side which adds depth to her character. And Robb Stark is portrayed as a strong - willed leader. It's a story full of emotions, from their loyalty to each other to the battles they fight side by side.