Izanami's Grief is a Sword Kit for Jin's katana and tanto. It is a reward for finishing the Mythic Tale "The Undying Flame", and like every kit it changes looks only.
Pick up the Mythic Tale "The Undying Flame" and see it through to the end. The kit is handed over with the tale's other rewards, so there is nothing to hunt for afterwards.
Izanami is the Shinto goddess of creation and death.
Only three Sword Kits come from Mythic Tales, so this is one of the rarer looks for your blades.