We have a number of requests in Pokemon Legends: Arceus. Here you are facing the headache that struck Psyduck in request 32.
Request 32 The Headache Stricken Psyduck Guide Pokemon Legends Arceus
This request is given to you by Martia, she is from the Diamond Clan and lives with Psyduck.
She will ask you to help her find a medicine that would help with the chronic headaches that Psyduck suffers from.
So what can you do? Go to Jubilife Village at the Galaxy Hall house. Find the medical room and talk to Tomma inside, she will give you a secret medicine.
Then, get out of here and head to Martia and her Psyduck. She will give the medicine to Psyduck and this will end this request.
To be honest, it is a bit strange to reduce the headache of this Pokémon because he is the strongest when he has a headache. But still, it is a request and this is the way to finish it.