It could be that Percy is being chased by some powerful enemy from his world and he stumbles into the Avengers' territory. His sudden appearance and the panic that follows draw the Avengers' attention. The 'atr' might be related to a special power or ability that Percy discovers in this new situation. This new power could be the key to defeating his pursuers, but he has to convince the Avengers to trust him first.
Obviously, Percy would be one of the main characters. He brings his own set of skills and experiences from his world. And of course, the Avengers. Maybe Tony Stark would play a major role as he is often the one to analyze new situations and technologies. Thor could also be important as he has some knowledge of magic and other realms which might help in understanding Percy and the 'atr' aspect.
To make it interesting, you can focus on the contrast between Percy's world and the Avengers'. For example, Percy's magic from the Greek gods is very different from the technology and superpowers in the Avengers' universe. When a panic attack occurs, this contrast can be highlighted. Maybe Percy's way of dealing with the panic attack is through some ancient Greek ritual, which the Avengers find strange but effective.
Well, a great Percy Avengers panic attack fanfiction could be centered around Loki. Imagine Loki, who is always so in control, having a panic attack after a failed scheme. Percy, being a demigod used to the treachery of the gods, understands his state of mind. He uses his knowledge of Greek magic and psychology to calm Loki down. Or perhaps it's a story where the Avengers are facing a new threat that is somehow related to Percy's world. The stress of this unknown danger causes one of the Avengers, like Natasha, to have a panic attack, and Percy has to step in to assist.
Annabeth would be a likely helper. She's very perceptive and has been through a lot with Percy. She would probably be able to sense something was wrong and offer her calm and rational presence to help him through it. Grover could also be there. He's Percy's loyal friend and his empathy for Percy's situation would make him a great support. He might even use his nature - related powers to create a more soothing environment for Percy.
One possible fanfiction could be Percy having a panic attack during a battle. Maybe he's facing a new and extremely powerful monster that reminds him of past traumas. He starts to hyperventilate, his hands shaking as he tries to grip his sword. His friends notice but are momentarily too occupied to fully assist him, adding to his sense of isolation and fear.
One common theme is friendship. His friends often play a crucial role in helping Percy through his panic attacks, showing the importance of support systems.
Another option could be Black Widow. She's very good at adapting to new situations and using her skills in different ways. For Percy, who is coming from a very different world, she could teach him how to be stealthy and use his powers in a more covert way. She could also help him with understanding the political side of the Avengers, like dealing with government agencies and such, which Percy may not be used to in his world of demigods.
Well, it could go either way. If the writer wants to create an interesting twist, Percy might be a villain in the Avengers fanfiction. But more often than not, given Percy's own heroic traits from his original story, he'd probably be a hero in the Avengers' universe, helping the Avengers fight against their common enemies.
Well, it could be about Percy being in a very stressful situation like facing a powerful enemy he's not sure he can defeat. This causes him to have a panic attack. Maybe he starts hyperventilating and his friends have to come to his rescue and calm him down.