The Hero of Tsushima Helmet is part of the Hero of Tsushima Armor bonus. If your edition includes it, it unlocks after the Prologue.
Own one of the editions with the Hero of Tsushima Armor and finish the Prologue. It is added for you.
Gosaku's Helmet - Improved
Gosaku's Helmet - Improved is a helmet that unlocks when Gosaku's Armor reaches level II. Upgrade the armor and it is added to your gear.
Gosaku's Helmet - Refined
Gosaku's Helmet - Refined is a helmet that unlocks when Gosaku's Armor reaches level III. Upgrade the armor and it is added to your gear.
Helm of the Lower World
Helm of the Lower World is a helmet hidden on Iki Island. It sits in a secret storage room on the Mongol warship you dock during "Jin from Yarikawa", at Fune's Refuge.
Helm of War
Helm of War is a helmet earned by finishing the Shrine of Ash, one of the Wind Shrines. The same shrine hands out the Spartan mask, so you get a full look in one run.