Gjallarhorn quest outline
This questline actually kicks off shortly after finishing the campaign. Speak to Shiro-4 and he'll give you the Echoes of the Past mission.
You're going to need a Splicer Key to complete the quest. If you don't have one, head into the Plaguelands patrol for the mission and start mowing down Broodmothers (Hive Witches). There's one to the right of the spawn point which is handy.
With your Splicer Key in hand, head to The Archon's Keep and look for the Patrol icon that looks like a Ghost.
Following the objective will lead you beneath Archon's Forge. You'll need to Splicer Key to take down the laser grid blocking the path.
This step in the mission culminates in a fight with a Fallen Walker. Once it's down you'll scan a wolf medallion in the back right corner and head back to the Iron Temple to talk to Lord Saladin and Tyra Karn.
Tyra Karn will give you the Beauty in Destruction quest and you'll need to ferret out seven Iron Medallions - which is where we come in to lend a hand.
Return to her once you've collected all seven and she'll send you to Bannerfall for the next quest, A Symbol of Honor.
When you're done, return to Tyra and she'l ask you for five SIVA clusters. Hand them over, and talk to Saladin for the final quest Beauty in Delivery.
Your reward at the end of this mission is the Gjallarhorn. Phew!