One scenario could be that Goku surprises Beerus with his speed and initial attacks as SSJ4. But then Beerus counters with his hakai and forces Goku to dodge constantly. Another could be that Beerus underestimates Goku at first and Goku manages to land some powerful blows.
Well, in many fanfictions, SSJ4 Goku is often depicted as having a chance against Beerus. SSJ4 Goku has shown incredible strength and combat skills. But Beerus has the power of a God of Destruction. His hakai ability could potentially wipe Goku out. Still, if the fanfiction is written in a way that gives Goku some new power - up or a special advantage, he could win. It really depends on the creative direction of the fanfic writer.
In a 'Goku vs Beerus' fanfiction, it's really hard to say who would win. It could depend on how the author wants to write it. If the author wants to show Goku's growth, Goku might win through some new transformation or power - up. But Beerus is a powerful God of Destruction, so he also has a great chance of winning.
There could be a storyline where Beerus, out of boredom, decides to train Goku Black instead of fighting him. But Goku Black misinterprets this as a sign of weakness and attacks Beerus. This could lead to a battle where Beerus has to hold back at first to avoid killing Goku Black, but as the fight progresses, he realizes he has to use his full power to subdue him.
One interesting plot twist could be that Goku and Beerus end up teaming up instead of fighting. Maybe they discover a common enemy that is even more powerful than them. Another could be that Beerus loses his power temporarily and Goku has to protect him from other villains while also trying to figure out how to return Beerus' power.
Goku being born with SSJ4 in fanfic would likely make him a force to be reckoned with from infancy. This could result in quicker power-ups, different battles, and maybe even a shift in the balance of power among the characters.
One possible plot could be Goku from the SSJ4 form crossing over into the world of Dragon Ball GT. He could encounter new threats that require his ultimate form to defeat. Maybe he teams up with the other Z - fighters in that universe to face off against a powerful and ancient evil that was sealed away long ago and has now been unleashed.
The plot might involve Goku SSJ4 teaming up with some unexpected allies in the Tournament of Power. He could be using his SSJ4 powers in creative ways, like combining them with the techniques of his new allies to gain an edge over the other universes' competitors.
Well, it could be a story where Female Beerus takes Goku on a journey through different universes to find a special kind of food that only exists in a very remote place. Along the way, Goku trains in new ways under Beerus' watchful eye. They encounter various challenges and obstacles that test their skills and their relationship.
In this kind of fanfiction, the power hierarchy in the Dragon Ball universe would be completely shaken. Goku's victory over Beerus could inspire other characters to strive for greater power. New alliances might form, and old ones might break. The Z - fighters could see Goku in a new light, either as a hero or a potential threat. The story could also explore Goku's moral compass. Killing Beerus, a god, might make Goku question the limits of his power and the responsibility that comes with it. There could be a lot of internal and external conflicts that make for an exciting fanfiction.