Well, a great plot for Supergirl Arrow crossover fanfiction could be centered around a common enemy from another dimension. This enemy has technology that nullifies Supergirl's powers and Arrow's skills, so they have to rely on their wits and each other's unique strengths. For example, Supergirl could use her heat vision in a creative way to expose the enemy's weaknesses while Arrow uses his archery skills to set up distractions. They could also meet some interesting characters from the other dimension during their adventure.
One idea could be that an alien threat emerges which requires the skills of both Arrow's team in Star City and Supergirl in National City. They have to combine their combat styles, with Arrow's more grounded and stealthy approach and Supergirl's super - powered attacks. For example, Arrow could use his trick arrows to create distractions while Supergirl takes on the stronger alien foes directly.
One idea could be that a powerful villain threatens both Star City and National City simultaneously. Arrow and his team are struggling with the more street - level threats in Star City, while Supergirl is dealing with the super - powered aspects in National City. Eventually, they cross paths when the villain's plan connects the two cities. For example, the villain might be using some sort of technology that is affecting the meta - humans in National City and also causing chaos in Star City's criminal underworld.
One idea could be that a powerful villain from another dimension is trying to take over all three of their cities simultaneously. The Supergirl, Flash and Arrow have to team up, each using their unique abilities. Supergirl could use her super strength to take on the villain head - on, Flash could use his speed to disrupt the villain's plans and steal important items, and Arrow could use his archery skills to set up traps and distractions.
In a fanfiction, there could be an alien race that is immune to Supergirl's powers but is vulnerable to the speed force. Flash discovers this during a battle where Supergirl is struggling. He then uses his speed to create a barrier around the aliens, trapping them long enough for Supergirl to figure out a new way to defeat them, like using her super - breath in a new way that Flash helps her direct with his speed.
One idea could be that a powerful villain creates a time - space rift that pulls both Supergirl and Flash into an alternate dimension where they have to team up to find a way back home. Their powers work differently in this new dimension, and they have to learn to adapt quickly.
Maybe there's a time - traveling mishap that brings Flash and Supergirl to an alternate universe where their powers are reversed. Flash has to deal with super strength and heat vision, while Supergirl has to learn to control super speed. They must figure out how to get back to their own universes and in the process, they bond over their shared confusion and determination.
One idea could be that the Flash and Arrow team up to stop a meta - human who has the ability to control time. They have to race against the clock (literally) to figure out how to neutralize the villain's powers before he rewrites history in a way that destroys Central City and Starling City.
One idea could be that Batman and Arrow team up to take on a common enemy like Ra's al Ghul. Since both of them have had run - ins with him in their respective storylines, it would be cool to see them combine their skills and resources to fight against him. Another plot could involve a mystery that spans both Gotham and Star City. Maybe there's a new criminal organization that's using technology from both cities to carry out their evil plans, and Batman and Arrow have to figure out how to stop them while also dealing with the differences in their methods of crime - fighting.
A great plot could involve the two heroes swapping cities for a while. Arrow tries to deal with Gotham's crime underworld while Batman goes to Starling City to investigate a series of strange disappearances that might be linked to a powerful criminal organization there. This would lead to both heroes having to adapt to different environments and crime - fighting styles.
One idea could be that the characters from Torchwood and Arrow team up to fight a common enemy that has some sort of interdimensional powers. Maybe a villain from Arrow's world has found a way to access Torchwood's technology and is using it for evil, and the two groups have to combine their skills to stop it.