In the realm of "who would win in a fight" debates, characters like Batman from DC Comics and Goku from the Dragon Ball franchise are constant fixtures. However, it is rare that the two will be paired against each other in such hypothetical matches. After all, Batman is a normal human with no powers whereas Goku is so powerful that, by Dragon Ball Super, he's literally on par with gods. Surely, Batman would have zero chance against someone like Goku, right? However, as characters like Darkseid and Superman can attest to, it's never a great idea to count Batman out on physical strength alone.
In terms of raw power, Goku outclasses Batman by several magnitudes. An argument could be made that Goku might be more powerful than anyone in the DC Universe. Even Batman's famous "Hellbat" armor likely wouldn't be able to bring the Saiyan warrior down. If Batman tried to defeat Goku by sheer physicality, he would lose plain and simple. However, Batman doesn't get included in these fight debates for his strength but for his intellect, where Goku's lack of smarts is well known among fans. As such, if Batman were to triumph against an opponent such as Goku, he'd have to rely on his wits to win the day.
An oft-repeated phrase for Batman fans is that he can beat anyone "with prep time" and it's likely that the Dark Knight's best chance against Goku would involve a lot of preparation and observation. In this regard, Batman's lack of power would actually be a benefit as Goku's ability to "sense" power levels would be ineffectual in knowing when Batman is observing him. In this way, Batman could collect information and data on him to look for weaknesses. For example, when Goku returns to Earth after the Frieza Saga, he is told by a time-traveling Trunks that he will die from a virus. If Batman were able to learn this information, he could easily apply his scientific acumen to creating a virus that could take Goku down without throwing a single punch.
The Dragon Ball franchise has shown their Earth has resources to build synthetic creatures with the ability to fight warriors on the level of Goku and his friends such as Android 17 and Cell. Batman certainly has the money, means, and mental acumen to build AI like Brother Eye. The resources afforded to him by the Dragon Ball world would certainly give him the potential to create a being he could use to incapacitate Goku. There are also the mystical objects of the series' name, the Dragon Balls, that Batman could collect to grant himself a decisive advantage, whether it be to power himself or to de-power Goku to even the odds.
Even without the idea of prep time, Batman still might have a chance to defeat Goku in some way. For all his power and strength, Goku has a code of honor in battle mixed with a general naïveté that makes him ripe for manipulation by his craftier enemies. As the master of mind games, Batman's greatest strength plays well with Goku's greatest weakness and he could either trick Goku into handicapping himself or pit Goku against an enemy better suited to fight the Saiyan to buy himself some time.
While an outright fistfight with Goku would leave Batman severely outclassed, the Caped Crusader is far too smart to put himself in that situation. Should the scenario arise, Batman would certainly rely much more on his brains than his brawn in defeating Goku. In the right writer's hands, the door is open for a victorious Dark Knight.