Spartan is a mask you earn by finishing an activity rather than picking it up. Complete the Shrine of Ash (a Wind Shrine) and it joins your gear.
Complete the Shrine of Ash (a Wind Shrine). The Shrine of Ash also gives the Helm of War and the Ghost of Sparta dye for the Sakai Clan Armor.
Adachi Dragon Mask
Adachi Dragon Mask is a New Game+ mask sold by Baku the Voiceless for 5 Ghost flowers. It does not exist in a first playthrough.
Adachi Half Mask
Adachi Half Mask is a mask you get by finishing "The Sister Betrayed", from Masako's tales, part 9 of 9. It is a story reward, so playing the tale is the only way to add it.
Ancient Dragon
Ancient Dragon is a New Game+ mask sold by Baku the Voiceless for 5 Ghost flowers. It does not exist in a first playthrough.
Avenging Lord
Avenging Lord is a mask waiting at a Gift Altar once you finish "The Broken Blacksmith" in Jin's Journey. Each main story milestone unlocks a different altar mask.