Since this sidequest involves taking photos, you need to have completed the main quest "Locked Mementos". Learn more about it here.
Talk to the group of NPCs at Serenne Stable and Akrah, the leader, will tell you about their research into ancient leviathans and their extinction. Using your Sheikah Slate, he asks you to take photos of leviathan remains on their behalf.
There are three skeletons you need to find, the Gerudo Great Skeleton, the Eldin Great Skeleton, and the Hebra Great Skeleton. Make sure you include the entire skull in your photo.
The Gerudo Great Skeleton is located to the extreme southwest corner of Hyrule. It is on top of the Great Fairy Fountain there and also the Hawa Koth Shrine. From Gerudo Town you can ride a Sand Seal southwest. Even through the sandstorm, do not budge and aim to go straight southwest never turning. You will eventually hit the edge of the map.
The Eldin Great Skeleton is located northwest of Death Mountain near the East Deplian Badlands.
Finally, the Hebra Great Skeleton stretches above the To Quomo Shrine in the Hebra region. So if you have discovered the To Quomo Shrine, you’ve already done the hard part. Just fast travel there.
If not, look for a very small, tiny pond east of Hebra North Summit and west of Gellam’s Secret Hot Spring. It is extremely tiny and is not visible on the map until you have zoomed all the way in. Go there.
You will then see past this pond a door. Use Cryonis to place two ice blocks in the tiny pond, forming a little "ice bridge" across it. Then run up the hill and grab a snowball. You will have to grab the biggest one you can pick up, or else it won’t be big enough to knock down the gates. Drop it down at the edge of the little cliff they are on and you will be able to go underground. Take a picture of the great skeleton from a distance so you can fit the skull into the frame.
Once you have a photo of all three skeletons, you can return to the Serenne Stable. You will have to show each photo to each of the three scientists individually. After that, Akrah will give you his promised gold Rupee worth 300 Rupees. Hopefully they don’t argue too much over these photos.