This page of our Call of the Sea guide details the location of all the secrets available in Chapter 1 - 74 Miles East of Otaheité.
Chapter - Chapter 1: 74 Miles East of Otaheité.
Location - in the water, just past the cliff.
You will find the barrel in the water, on a beach full of signs and symbols. You only need to climb a rock (there may be a parrot sitting on it). At the top, look down. You won't fall, so you can take a good look at the barrel.
At this point, you can get an achievement!
When you examine the barrel, you will get the "a Brigantine, a Brig and a Barque" achievement.