Return of the Obra Dinn

All 60 fates in order of discovery are;

Chapter X

William Hoscut (Outside Captain's Quarters) - Shot with a Gun by Robert Witterel.
Henry Brennan - Knifed by Robert Witterel.
Lewis Walker - Clubbed by Robert Witterel.
Robert Witterel - Suicide by Gun.

Chapter VII

Abigail Hoscut Witterel (Inside Captain's Quarters) - Crushed by Rigging.
Maba - Torn Apart by Beast.
Peter Milroy - Exploded.
Roderick Andersen (Under a Cannon, North East corner of Gun Deck) - Crushed by Cannon.
Christian Wolff - Shot with Cannon by Beast.
George Shirley (No corpse, same page as Wolff) - Shot with Cannon by Beast.
Abraham Akbar - Crushed by Beast.
Edward Spratt (Far right of Gun Deck) - Crushed by Beast.
Lars Linde - Clubbed by Nathan Peters.
Omid Gul (First disappearance of Chapter VII) - Drowned by Beast.
Nathan Peters (Second disappearance of Chapter VII) - Drowned by Beast.
Alexander Booth (Third disappearance of Chapter VII) - Drowned by Beast.
Duncan McKay (Fourth disappearance of Chapter VII) - Drowned by Beast.
Wei Lee Fifth disappearance of Chapter VII) - Drowned by Beast.
Finley Dalton (Sixth disappearance of Chapter VII) - Drowned by Beast.
Charles Miner (Seventh disappearance of Chapter VII) - Drowned by Beast.

Chapter IX

Thomas Lanke (Midshipmen's Quarters) - Knifed by Olus Wiater.
John Davies - Clubbed by Henry Brennan.
Olus Wiater - Shot with a Gun by John Davies.
Leonid Volkov - Shot with a Gun by Emily Jackson.
Paul Moss - Killed with a Sword by Leonid Volkov.
Alfred Klestil - Torn Apart by Beast.
Emily Jackson (First disappearance of Chapter IX) - Alive in Africa.
Miss Jane Bird (Second disappearance of Chapter IX) - Alive in Africa.
Davey James (Third disappearance of Chapter IX) - Alive in Africa.
Henry Evans (Fourth disappearance of Chapter IX) - Alive in Africa.

Chapter III

Timothy Butement (First Mate's Quarters) - Shot with a Gun by Edward Nichols.
Hok-Seng Lau - Shot with a Gun by Henry Brennan.
Nunzio Pasqua - Knifed by Edward Nichols.

Chapter VI

Zungi Sathi (North side exterior of Orlop Deck) - Shot with a Gun by Charles Miner.
Emil O'Farrell - Spiked.
Charles Hershtik - Burned.
James Wallace - Decapitated by Beast.
Jie Zhang - Decapitated by Beast.
Marcus Gibbs - Spiked.
Nicholas Botterill - Speared by Beast.
Huang Li - Electrocuted.
Winston Smith (Bosun's Store on Cargo Deck) - Speared by Beast.

Chapter V

John Naples (North West corner of Cargo Deck) - Killed with Sword by Fillip Dahl.
William Wasim - Crushed by Cargo.
Thomas Sefton - Struck by Tail.
Chioh Tan - Spiked.
Hamadou Diom - Spiked.

Chapter IV

Edward Nichols (North side of Main Deck)- Shot with a Gun by Chioh Tan.
It-Beng Sia - Burned.
Bun-Lan Lim - Clawed.
Samuel Galligan - Knifed by It-Beng Sia.
Patrick O'Hagan - Speared by Beast.
Li Hong - Speared by Beast.
Aleksei Toporov (First disappearance of Chapter IV) - Drowned by Beast.
Alarcus Nikishin (Second disappearance of Chapter IV) - Drowned by Beast.

Chapter II

Investigate the Cow Skull, North side of Orlop Deck.
Renfred Rajub - Illness.
Solomon Syed - Illness.

Chapter I

Investigate the Cargo in the North East room of the Cargo Deck.
Investigate the next body, but leave the ship before solving the fate to unlock;

Rewind back onto the Ship.
Samuel Peters - Crushed by Cargo.

Chapter VIII

Martin Perrott - Spiked
Fillip Dahl - Burned

The chapters can be found in a different order, but this is a fairly smooth way of getting through them all.

In this video I walk you through the game to get all the achievements in one playthrough

Achievement Walkthrough: