Avenger's Ashes is a relic piece obtained by defeating Shura, the 2nd Boss in the Canyon of Immortality. Alternatively, you can purchase it from the Adventure Store for 650 Smith Tokens.
The Avenger's Ashes is the core component in the Relic Fusion to create the Artifact Sword, Avenger, the Twinblade (110 AP & 5 DP, Wind).
The other pieces you need to create Avenger, the Twinblade are the 3 Rank-A Adamantite swords; Heldon, Lionheart, and Musou (Adamantite). As you can see in the below picture, it will tell you how many correct swords you have. The below picture has none with a gold border, so it still needs all 3 Rank-A swords.
Successfully fusing the 4 components together for 48 hours will result in your sword.
