This guide focuses on how to evolve Ponyta in Pokemon Legends: Arceus. To evolve Ponyta into Rapidash, all a player needs to do is raise it to Level 40. Once that threshold is reached, the player can head over to the Party Screen and tap the Flashing Pokeball in order to Evolve a Ponyta. Once the Ponyta has reached Level 40, Ponyta can Evolve to a Rapidash. Select him, then hit evolve, after which your Pokemon will transform into a Rapidash.

Rapidash appears as a Level 40 Alpha Pokemon on the Plains of Horseshoes, located within the Fieldlands of Obsidian. Once the level on your Ponyta has been reached, you must head over to your Party Panel tab, and choose the Ponyta.
Your Ponyta is different from many other Pokemon since the Ponyta does not need any Evolution Stones to evolve. The shiny Ponyta evolved to Rapidash at level 40, with its shiny blue flames being replaced by grey ones, while Rapidash gained stronger features. Alpha Rapidash is at level 40, meaning that it has only evolved, and it is capable of taking down any starting Pokemon that may have been in your party.
This spot you found Ponyta was seen at the start of Pokemon Legends, however, now you will want to watch out for running into Alpha Rapidash, which has no trouble taking out beginner players. It goes without saying that the player has to catch a Ponyta before they can turn it into a Rapidash.

Upon finding the peculiar Ponyta, merely requires skulking, catching it using any means preferred, then returning it to the NPC named Yota. Players need only to throw a Pokeball, of whatever kind, to a blue-mans Shiny Ponyta, who happily accepts being caught.
Once you capture the Pokemon and return to Yota, she lets you keep the Ponyta and gives you five Razz Berries, either restoring Pokemon HP or making wild Pokemon slightly easier to catch. An NPC named Yota lets you keep the peculiar Ponyta, and he will even give you five Razz Berries which you can give wild Pokemon to make them easier to catch for your troubles.
Get her battles level her up and when she is ready, head to the Plains of Horseshoes and search for a Ponyta; you will want to stealthily get up close so that it does not escape. The Pokeball near your Ponyta should flash, showing that it is ready for evolution.