Yes, there are likely 'Ash Catches Rayquaza' fanfictions out there. Fanfiction writers often create stories based on popular Pokémon concepts like Ash catching a rare and powerful Pokémon like Rayquaza. You can try searching on fanfiction websites such as FanFiction.net or Archive of Our Own to find such stories.
One possible plot could be that Ash hears rumors of Rayquaza's appearance in a far - off region. He sets out on a journey with his Pokémon friends. Along the way, he has to face various challenges and other trainers who also want to catch Rayquaza. Eventually, he uses his unique bond with his Pokémon and his strategic skills to outwit Rayquaza and catch it.
In many Pokemon fanfictions where Ash catches Machop, it often shows Ash's growth as a trainer. Maybe he discovers Machop in a unique situation, like in a hidden valley. Machop is a strong and determined Pokemon, so when Ash catches it, it could potentially become one of his most powerful allies. It might be a story full of adventure and challenges as Ash tries to train Machop and bond with it.
In the fanfiction, Misty catches a Pokemon that has a special ability. Ash, being the competitive trainer he is, challenges her to a battle right away. The battle unfolds in a unique location, perhaps near a waterfall. Ash sends out his Charizard, and Misty uses her newly - caught Pokemon. The clash between fire and water - based attacks creates a spectacular scene.
One possible scenario in this fanfiction could be that Ash encounters Mewtwo in a new, uncharted region. Mewtwo, being intrigued by Ash's unwavering spirit, decides to test him. Ash passes the tests with the help of his Pikachu and other Pokemon. This leads to Mewtwo seeing Ash as a worthy trainer and allowing itself to be caught. It would be a great twist on the usual Pokemon-catching storylines.
In many fanfictions where Ash catches Lugia, it often involves a great adventure. Maybe Ash stumbles upon Lugia in a hidden cove. Lugia, being a powerful and majestic Pokémon, would be a huge addition to Ash's team. It could change the dynamic of his battles completely. He might have to prove himself worthy to Lugia first, perhaps by showing his kindness and determination in protecting other Pokémon in the area.
The plot could involve Ash hearing rumors about Mewtwo's location. He sets out on a journey to find it. Once he does, he tries to communicate with Mewtwo. Mewtwo initially resists but Ash's pure intentions start to sway it.
One of the best moments is when Ash finally manages to catch a Celebi in some fanfics. The build - up to that moment, with all the time - traveling adventures and the connection he forms with Celebi, is really thrilling.
Obviously, Ash is one of the main characters. He is the trainer who catches the shiny Pokemon. His Pikachu also plays a significant role, as it's always by Ash's side and could potentially have some interesting interactions with the shiny Pokemon.
A plot might be that Lugia is being hunted by an evil organization. Ash discovers this and decides to protect Lugia. He uses his Pokémon to fight off the bad guys. In the process, he forms a bond with Lugia. Eventually, Lugia realizes that it's safe with Ash and allows itself to be caught. This would show Ash's heroism and his love for Pokémon.