In Pokémon Legends: Arceus, Miki from the Security Corps tells you that children have been spotted playing with Drifloon at night and she sends you to investigate.
In order to grab the request and start it, head to the Galaxy Hall. In the room where the Professor stands, there will be a chalkboard right behind him. There are several requests you can pick up there, and Playing with Drifloon is one of them. This request is unlocked after you’ve caught a Drifloon.
It’s been reported that children from the village have been sighted playing with Drifloon at night and Miki of the Security Corp sends you to investigate. The children have been spotted playing with the Pokémon at night down by Prelude Beach.
This request is pretty easy to complete. If it isn’t evening yet, head to your house and go to bed. Select “sleep until evening” and then when you wake up, the time will be set to evening and you’ll be able to head to the beach to investigate.
Drifloon and the child will be behind the small shack down by the beach. The child will tell you that Drifloon wouldn’t let him leave, but that the Pokémon didn’t mean to be bad. Head back to Miki to complete the quest and you’ll be rewarded with Stardust.