Week 2’s Ascendant Challenge (which you can buy from Petra) again revolves around dealing with the Taken, but the particulars of what you’re doing are entirely different. To start out, you’ll need a consumable item called the Tincture of Queensfoil. These can be obtained in a variety of ways while in the Dreaming City; you can open chests and complete Public Events, for instance.
However you obtain it, your next step is to head for the Garden of Esila area near the bottom of the map, as seen in the image below. Consuming the Tincture of Queensfoil will provide you with a buff that allows to see a Taken portal that’s somewhat hidden on a cliffside. Jump in, and you’ll be teleported to the Ascendant Plane’s Forfeit Shrine.
Once you’re there, you’ll have to fend off Taken–or just avoid them–while trying to secure three Arc Charges around the area. Grab one and make your way back to the center area, near the giant Blight ball. Underneath that is a bright point; walk over it with the Arc Charge to dunk it. Repeat the process two more times and you’ll receive Super energy that will help you to kill all of the remaining Taken. Manage to survive that, and you’ll complete the bounty (netting you Dark Fragments and Powerful gear) and receive a chest to open.
Given that the bounty (not the chest) offers Powerful gear–a reliable way of increasing your Power level–this is an activity you’ll definitely want to take part in once you’re able. But bear in mind it is a challenge, so be sure to come prepared.