Talk to Kanae Urabe located in the Daitama Observatory to receive this quest. Next, head to the Illusionary Daitama idolasphere. It's entrance is located to the far right of the same location. Once inside, head to the first elevator and down to the lower level. You'll find a shining object on the ground. Pick it up to get a Treasure Key then report back to Kanae to complete this request.