The Bad Juju is back in Destiny 2. The never-ceasing Exotic Pulse Rifle can be yours, if you please Calus. To start off the quest, go and visit Werner aboard the Imperial Barge on Nessus. Beside him, you will notice a new Imperial Chest that costs 5000 Glimmer to open. Open it up, and you will get an Imperial Invitation to the The Tribute Hall!
The Tribute Hall is a new area on the Leviathan that Calus has built as a monument to his love and respect for Guardians. You can get to it by opening your Director, going to Nessus, then scrolling down to the Leviathan.
Bad Juju Quest Guide
When you arrive in the Hall of Triumph you will need to interact with the large statue of Calus. You will then be able to get some daily bounties to start working on. For the next step in the quest, you need to complete any one of those bounties. I just did the one that asks you to kill 50 enemies without dying. When you hand it in, you will get a Boon of Opulence that you can then return to Calus at the Tribute Hall.
When you do this, you will receive a Tribute that you can place to open the main door, to get access to the main Tribute Hall. In here there will be lots of slots that you can place Tributes in.
Now, to get your hands on Bad Juju, you will need to stay placing Tributes, and will also need to place five Beast Tributes in the center of the room that you will get automatically as you place set numbers of other Tributes. You will need to place a total of 18 Tributes in the main Tribute Hall, including the five Beasts.
When you have placed all five Beasts, you can return to Calus who will have a new mission for you. Go to the weird chest in the center of the room and interact with it, and you will begin a mission in the Ascendant Plane. When you complete this mission, you will get the Bad Juju!
If you have a lot of materials saved up, then now is your time to shine, as you can actually buy Tributes from the statue of Calus! This seems very fitting for the Emperor, who builds us a Tribute Hall in our honor then charges us Glimmer and materials to actually fill it with nice things!
Now, this is a fairly truncated guide at the moment, drawn together from my own progress and from various others who are playing the game right now. But basically if you want the Bad Juju, you will need to get grinding Tribute Hall Triumphs that you can find under the Destinations section of the Triumphs tab! The sooner you get through them, the sooner you get the Bad Juju!