Instructions
Fight the Abyssal Gladiator, located after the caves of the Ashlands. Save your Chaos form until you pull the Gladiator off his steed. In this form, Wrath will quickly defeat the Abyssal Gladiator and get back his horse, Ruin, as a prize.
Ride south on Ruin and defeat the foes along the way. Of note among these foes is the Ash Titan. While on Ruin, use Mercy to shoot the titan's mouth a few times and activate the prompt that appears over its head to defeat it. Exit through the northern area.
After ditching Ruin, you need to beat a Devastator with a cannon. Defeat it with your Wrath powers and use the cannon to blast the other enemies. Leave the cave.
Head out into the open to defeat Stygian. Destroy the cage-like muzzle on its mouth by riding alongside it and slashing it with your sword. After the muzzle is destroyed, use Mercy to fire at the mouth while keeping your distance. After it burrows the second time, keep firing on the mouth with Mercy, and a prompt will appear over its head. Activate it to defeat Stygian.
Use a Vulgrim location to head back to Samael and give him the Heart of the Chosen. Use a Vulgrim location to head back to the entrance of the Ashlands.
With Ruin, head north across the desert past the Wooden Towers. Look to the northeast to spot some blue crystals. Smash them and enter the cave to find the Wrath shard. (Note that this is only possible after Ruin is acquired and heading back to the entrance of the Ashlands.)