Here is the full list of all 16 Return of the Obra Dinn achievements. It takes around 10-12 hours to unlock all of the achievements on Windows.
Solve the entire book.
Solve all fates in chapter VI.
Solve all fates in chapter VII.
Solve all fates in chapter V.
Solve all fates in chapter IX.
Solve all fates in chapter IV.
Solve any 45 fates.
Solve all fates in chapter III.
Solve all fates in chapter X.
Solve all fates in chapter I.
Solve all fates in chapter II.
Solve any 30 fates.
Solve any 15 fates.
Solve any 6 fates.
Loosely true, in the eyes of Company and Crown.
Leave the ship without solving all available chapters.