Legendary Rabbit Trial
Once you have begun the main quest "The Hero's Sword" and have unlocked your Sheikah Slate's camera by completing the main quest "Locked Mementos", you can begin this sidequest. You can learn more about The Hero's Sword and Locked Mementos by clicking on their respective links.
Talk to Peeks, a small Korok in Great Hyrule Forest wandering around near Chio and Kula. Peeks wants a photo of a Blupee. Like other photo-related sidequests, a photo in your Hyrule Compedium won't do. You have to have the photo in your Album.
The easiest Blupee to find is right outside Kakariko Village by the Great Fairy Fountain. Sneak up on the Blupee to get a good picture of it. Alternatively if you see a green glow on top of Satori Mountain, you can go there and there will be herds of Blupees surrounding the Lord of the Mountain. But the green glow is very rare and random, so your best bet is Kakariko Village.
Once you have the photo, return to Peeks. As a gift of gratitude, Peeks will give you a silver Rupee worth 100 Rupees and will also tell you that Blupees drop Rupees if you hit them. They seem a bit too cute to smack though...