One idea could be to focus on Bardock's perspective before his fateful battle. Maybe explore his thoughts about his son Goku being sent to Earth and his own impending doom. He could have some premonitions about Goku's future role in saving the universe.
Another potential rival could be a young, prodigious martial artist from a new school of martial arts on Earth. This character could be jealous of Goku Jr's fame and constantly try to outdo him in battles and in the eyes of the public. He might use unorthodox techniques that Goku Jr has to quickly figure out how to counter.
Well, it could be about Goku Jr learning some of Goku's most powerful moves. Maybe Goku teaches him the Kamehameha. They might also go on an adventure together, like fighting a new and powerful enemy that neither could face alone.
To develop Goku Jr's character further, he could be given more complex emotions. For example, showing his fear in the face of truly overwhelming enemies, rather than always being fearless like Goku. This would make him more relatable. Also, exploring his relationships in more depth, like his friendship with Pan. Maybe they have a falling out over different views on how to protect their world, which forces Goku Jr. to grow and understand different perspectives.
Maybe an old enemy of Goku's who has somehow managed to return. This enemy has heard about Goku Jr and figures that by attacking him, he can get revenge on Goku. This could be someone like Frieza who has found a new way to be resurrected and is more powerful than ever.
Definitely include Bardock's last stand. His heroic yet doomed battle is a crucial part of the Saiyan lore. It could be written in great detail, with Bardock using his full power against Frieza's forces.
It could be that female vegeta has been training in a secret location with a unique training regime. This gives her an edge over goku in combat. For instance, she might have trained with some ancient master who taught her a special form of ki control that goku has not mastered yet. So when they face off, she is able to use this advantage to defeat him.
I'm not sure of a specific 'female vegeta beats goku fanfic' off - hand. You could try searching on fanfic websites like Archive of Our Own or FanFiction.net. They have a vast collection of Dragon Ball fanfics and you might find one that meets this criteria there.