The Golden Hamachou is one of the three secrets after getting the Swashbuckler Rating Vyse the Legend. It is located at peak of the mountain (technically in upper sky) on top of the archway island which the player passes through several times to reach Sailor's Island from Pirates isle. It is found like a Discovery but does not appear in your Journal and can't be sold. When found, the font reads:
A Bird-like unknown creature shining gold. They say that it is a hybrid between Hamachou and an ancient animal, but details are still unknown. If you are lucky enough to see this rare bird, your wish will be fulfilled.