The first thing that you need to do is visit Xur and purchase as many sets of the Three of Coins that you can afford. This will set you back 7 Strange Coins for a five pack. We started by buying four packs, giving us the Three of Coins buff 20 times.
Before you leave the Tower, make sure that the character you're using has a Rocket Launcher equipped, and that you are packing several packages of the Heavy Ammo Synthesis. These rockets are going to be the method that you use to kill Draksis, Winter Kell, as well as yourself.
Head to Orbit and load up a story mission called the Scourge of Winter. You'll have to slug through some of the level to get to the final boss, but for the most part you can just run past all of the enemies. For the ones you can't, you should be massively overpowered for them if you've spent much time at all in The Taken King.
When you get to the end a door will open at the top of some stairs and you'll be able to see Draksis, Winter Kell sitting inside. Before you go in, make sure that you have both Heavy Ammo, as well as the Three of Coins buff active. You can use the Three of Coins by going to your inventory tab and selecting it. Note that the Three of Coins is not on a timer, and will only expire if you kill an Ultra, such as this fool standing in front of you. As long as you see the multiplier for the buff on the character screen, it's active.
Sit just outside the room and snipe Draksis in the head until he has about 20 percent of his health. Clean out all the adds in the room using any weapon that you want, collecting any Heavy Ammo and House Banners that you can find. When the room is clear, head inside and pull out your Rocket Launcher. When Draksis approaches you, shoot him with a rocket, killing you both. The exotic engram (assuming one dropped) will be on the ground, but you can pick it up in a moment.
Since both you and Draksis died, the mission will reset from where you were just outside the door. The room will be full of adds again, but you can simply repeat Step 4 until you're out of the Three of Coins. You just want to make sure that any time you load back in at the checkpoint, you have Heavy Ammo and an active Three of Coins buff. From here you can repeat the process as many times as you wish.
Head back to the Tower and get the Cryptarch to decode the engrams for you. Even if you get one that you already have, check the perks to see which one you want to keep, and which one you want to dismantle. Beyond that, just do this as much as you can before Bungie patches it, because there is a 99.9 percent chance that they will do just that.
This process is likely to see changes throughout the day, so we'll point you to the same source in which we found it, a post on the Destiny Sub-Reddit.
For more content for The Taken King, visit out Destiny: The Taken King Walkthrough and Guide.