Loone wants to see the leviathan fossil in the Eldin region, which she marks on your map.

Quest Location

Talk to Loone at East Akkala Stable to start the quest.

Find the Eye

After you go to the leviathan location that Loone marked on your map (1673, 3683, 0099) talk to her and she points out that one of the leviathan's eyes is missing.

Go underneath the skull to find a pile of boulders. Get rid of those boulders (e.g. with bombs, heavy weapons, etc.) then use Ultrahand to move the eyeball (a round grey boulder) into the empty eye socket. It will automatically be pushed in if you do it correctly.

Quest Reward

Talk to Loone after you put the eye back in the socket, and you get 50 rupees.