Before we get into the Gjallarhorn exotic quest, I should note that this firearm is only available to those who purchased the Bungie Anniversary Bundle for $24.99. If you do not own this DLC, then this exotic rocket launcher is unobtainable.
1. Complete the Dares of Eternity and Grab the Quest from Xur
When you load into the game for the first time since the update, you will be thrust into the new Dares of Eternity activity. This is a six-man activity that acts like a game show for people who like to shoot aliens. Completing it for the first time will cause you to be whisked away to Xur's treasure room. Speak to Xur and then scroll to the second page in his vendor menu. You should see the quest there for you to grab. Now go visit Shaw Han in the Cosmodrome.
2. Complete the Grasp of Avarice
After speaking to Shaw Han, you'll be tasked with completing the new Grasp of Avarice dungeon. Set at 1310 Light, this is a fairly simple endgame activity. While some of the encounters can be a little tricky at first glance, you shouldn't have too much trouble once you get a handle on how each encounter plays out. Remember: There's no matchmaking for dungeons, so you'll need to find a fireteam. This dungeon has a bunch of puzzles, but only three core encounters — two of which are bosses. There's also a Sparrow section where you'll need to race to disarm mines before they explode.
If you don't want to go into the Grasp of Avarice dungeon blind, here's a full walkthrough of every major encounter!
4. Defeat 7 Powerful Fallen in the Cosmodrome
Once the dungeon is complete, you will need to go back to Shaw Han. He will inform you that you still need to reassemble this rocket launcher. To do so, you'll have to gather 7 Wolfpack Rounds, which are rewarded for killing powerful Fallen enemies in the Cosmodrome. The two best ways to do this are by either completing any of the Fallen-focused Public Events or going to Exodus Garden 2A Lost Sector in The Divide. Both are solid options and it only took me two runs of the Lost Sector to finish this step.
5. Complete the Exodus Garden 2A
After flying to The Tower and speaking to Banshee-44, you have one more real step left to earn the Gjallarhorn. Go back to the Cosmodrome and head to the Lost Sector shown above. You don't need to complete it on Legendary or Master difficulty, so go breeze through it. Once you defeat the boss, open the chest to finish this step. Now go back to Shaw Han and head into the small workshop directly across from where he's standing. You'll see a small workbench in the corner. Approaching it will prompt you to put the weapon back together, so just hold down Interact until the circle is completed.
Speak to Shaw Han for a final time to earn the exotic rocket launcher and scourge of LFGs everywhere, the Gjallarhorn!
How to Get the Gjallarhorn Catalyst
Before we get into how to get the Gjallarhorn catalyst, I want to give credit to Youtuber Newo for seemingly discovering this first.
Once you've earned the Gjallarhorn, you'll need to head back into the Grasp of Avarice dungeon. This can be on any difficulty and you need to at least complete up to the final boss. Your goal is to kill three yellow bar Reaver Vandals and deliver the Burden by Riches debuff they drop to three different chests scattered throughout the dungeon. You will not get anything for opening the first two chests, but unlocking the third one will reward you with the Gjallarhorn Catalyst.
You will find the first Reaver Vandal right after you enter the loot cave at the start of the dungeon. Along the narrow walkway in the cave, you will see the Reaver Vandal on the cliffs to the right. Killing the Vandal will give you the Burden by Riches debuff. Now turn around and run back the way you came towards the metal scaffolding. At the top of the scaffolding will be the chest. Open the chest while you still have the debuff.
The second Reaver Vandal can be found right after the large cylinder is rolled down the stairs in an attempt to crush you. Dodge this incoming trap and make your way to the room where you normally climb into the vent to progress further. Damage the Reaver Vandal on the left by some boxes until he drops an engram, then quickly go into the vent with your debuff. Go right, left, and then go immediately right along the wall when you exit the vent. You should see the chest on a small platform (shown above).
The final chest is only accessible after you've completed the Fallen Shield encounter. Head to the center island and, instead of launching yourself up into the massive hole you made, point the cannon towards the back of the room. Activate the gravity lift via the Scorch Cannon and rocket yourself to the other side of the room. You'll find the Reaver Vandal hanging around a small stream, so damage this enemy until he drops some engrams. Pick these up and make your way back to the center island. This can be tricky because you only have 30 seconds, so either have the cannon already pointed towards the middle island or pop Top Tree Dawnblade to fly over the gap.
If you're a Hunter or Titan I recommend having someone ready to launch you with the cannon to the center, otherwise, there's barely enough time.
Regardless of how you get to the center island, climb onto the roof of the large round building in the middle. You should see the chest. Opening it will reward you with the Gjallarhorn catalyst. Now you can either finish the dungeon or leave; it doesn't matter. When completed, this catalyst makes the rocket launcher reload faster and creates additional, stronger missiles whenever your Wolfpack rounds kill an enemy. To complete the catalyst, just kill 400 enemies with this rocket launcher in any activity!