The plot might involve Black Widow being sent on a mission to investigate some strange happenings that turn out to be related to the magic and mythology of Percy Jackson's world. Percy gets involved because he has knowledge of these things. They start off at odds but as they uncover the mystery together, they start to respect and rely on each other. Their different backgrounds - Percy from a world of gods and monsters and Black Widow from a world of superheroes and villains - would create a lot of room for interesting character development and plot twists.
One possible plot could be that Percy Jackson, with his water - controlling powers, gets transported to the Marvel universe. He meets Black Widow during a mission where they are both after a powerful artifact that has ties to both the Greek mythology in Percy's world and some secret Hydra project in the Marvel world. They start off as distrustful allies but gradually learn to work together and respect each other's skills.
One possible plot could be Percy finding out he has a connection to Black Widow. Maybe he discovers some hidden powers or abilities that are related to her skills. He could then face challenges in the demigod world where his newfound 'Black Widow - like' traits help him out, like enhanced combat skills or strategic thinking.
A plotline could involve Percy Jackson being sent on a quest that somehow involves the modern world and S.H.I.E.L.D., where Black Widow is involved. They meet, and Black Widow is initially skeptical of Percy's powers and claims. But as they face various challenges together, she realizes his abilities are real. The fanfiction could explore how their two very different worlds and personalities interact and eventually lead to a romantic connection. There could be elements of Percy teaching Black Widow about the demigod world and Black Widow showing Percy some of her spy skills.
A possible main antagonist could be a new character created specifically for this fanfiction. A scientist who has somehow managed to combine Greek magic with Hydra technology. This character could be creating powerful hybrid creatures that are causing havoc in both Percy's world and the Marvel universe. Percy and Black Widow would need to put aside their differences and work together to stop this mad scientist.
One idea could be that Black Widow is somehow transported into the Percy Jackson universe. Maybe she has to team up with Percy and his friends to defeat a common enemy. Since she has her combat skills and spy training, she could offer a different perspective on battle strategies compared to the demigods.
I'm not sure of specific fanfictions for this crossover. But you can try searching on fanfiction websites like Archive of Our Own. They have a large collection of fan - created works, and you might be able to find some interesting Black Widow and Percy Jackson crossovers there.
Percy would probably be in awe of Black Widow's combat skills at first. He might try to show off his own powers a bit, like making a small water show. Black Widow, on the other hand, would be cautious but intrigued by this strange boy with powers. She would likely start to analyze his abilities and how they could be useful in a fight.
One possible plot could be that the gods in the Percy Jackson universe sense a great threat from another dimension (the Marvel universe). Percy and his friends are sent to team up with the Avengers. Percy's water powers could be useful in fighting villains like Electro. Annabeth's strategic mind would assist in planning battles against foes like Loki. They all have to learn to work together, with Percy and the Avengers initially having some clashes due to their different ways of handling things.
One possible plot could be that Percy gets lost in a strange dimension and ends up in the Naruto world where he meets Tsunade. Tsunade initially doubts Percy but then realizes his powers when he shows his ability to control water. They then team up to fight a common enemy that is threatening both their worlds.
In this fanfiction, perhaps Gaea discovers a way to use the chakra in Naruto's world to strengthen her own power. She sends her minions to capture ninja who are strong in chakra. Percy Jackson, who has a connection to the spirit world, senses this disturbance and travels to Naruto's world. Naruto and Percy meet and realize they have to work together. They gather allies from both worlds, like Naruto's friends from Konoha and Percy's demigod friends, and fight against Gaea and her forces.