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.
I think it depends on various factors. Goku's determination and growth are remarkable, but Beerus has an overwhelming level of power and authority that might be difficult to overcome.
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.
In Dragon Ball fanfic, Goku SSJ often has super strength, like being able to lift extremely heavy objects with ease. He can also move at incredible speeds, making it hard for enemies to even see him coming. His energy blasts are much more powerful than in his normal form, capable of destroying large structures or powerful foes in one shot.
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.