A villager by the name of Asabei is going through that exact same thing, and he asks for your help to help him find a Pokémon with an elegant tail that curls like a spring, catch it, and bring it back to him to show him. The Request is rather simple, and it won’t take long for you to finish. But truth be told, these requests or quests in Pokemon Legends Arceus are scarce on information or at least some knowledge of Pokemons.
Request 41 Elegant Tail Guide – Pokemon Legends Arceus
The Pokémon Asabei is talking about is called a Glameow, a cat-like Pokémon that is located in the Cobalt Coastlands near the very first camp. When entering Cobalt Coastlands, you’ll need to head towards the direction of the beach, down a slope towards Gingko Landing.
The exact location and area in which Glameow is known to appear is here:

The Glameow can be found on the very same slope, but be cautious when approaching it, as the Glameow will run away and disappear once it spots you.
Attempting combat with the Pokémon will result in the Glameow fleeing before you can even attack, so your best bet is to sneak up to the Pokémon and catch it with a Poké Ball.
Bear in mind that the Pokémon is most likely to appear during the day, but it could be there during night. Just to have a better chance, try looking during the day.
Once you have successfully captured the Glameow, return to Asabei and show him the spring trailed Pokémon and the Request is complete, rewarding you with 2x Aux Evasion and 2x Grit Gravel.
Now, the Glameow is not really a difficult to get Pokemon, but still, keep in mind that catching Pokemon in Arceus is a bit trickier than previous Pokemon games.