Betrayer's Hat is a straw hat you get by finishing "Shadow of the Samurai" in Jin's Journey. It is a story reward, so you cannot buy it.
Play the main story through "Shadow of the Samurai". The hat comes with the tale's rewards.
The hat belonged to Ryuzo, Jin's childhood friend, and its text brands him a traitor to Tsushima.
Ashen Straw Hat
Ashen Straw Hat is a hat that unlocks when you upgrade Ronin Attire to level IV. It is added automatically, so there is nothing to find in the world.
Bloodstained Betrayer's Hat
Bloodstained Betrayer's Hat is a New Game+ hat sold by Baku the Voiceless for 5 Ghost flowers. It is not available in a first playthrough.
Bone White Straw Hat
Bone White Straw Hat is a New Game+ hat sold by Baku the Voiceless for 5 Ghost flowers. It is not available in a first playthrough.
Bowman's Straw Hat
Bowman's Straw Hat is a straw hat favoured by archers. You get it by finishing "The Art of Seeing", the second of two Yuriko side tales.