From the starting point, head straight to the Warmind Bunker indicated by the objective marker on your map. If you don’t see one, bring up your Ghost and it should appear. You can actually ride your Sparrow while your Ghost is active if you need directions when traveling long distances. When you arrive, descend the stairs to the bunker, and notice the familiar interdimensional goo strewn about. Turns out sealing the complex didn’t stop the Taken from getting through.
Continue through the bunker, eliminating the various Taken Cabal along the way. This place should look familiar, as this is where Siege of the Warmind took place. You’ll reach a room where several more Taken Psions will spawn, as well as a Taken Centurion. Both of these enemies take critical hits when you shoot them in the head, but you need to watch out for the Psions, as they can hit you from a long way back. If you have a Titan in your group, it might be time for the Hammer of Sol.
Tip: This area is full of different things that you can scan with your Ghost. Ensure that you’re taking time to explore, as Rasputin’s bunker is one of the cooler environments in all of Destiny.
Locate a computer terminal you can scan nearby if you wish, and then head through the door just past the terminal on the left. Continue through the narrow corridors, fighting off a few more sets of Taken enemies. Pass through a straight hallway with several opening doors to reach the Mine.
Once you are at the Mine, vanquish the Taken Centurion and the handful of other Taken. Scan the terminals to Rasputin’s database and download the stealth codes to complete the mission.
Since that story mission was so short, you might as well continue to Destiny: The Taken King: Last Rites, or return to the Destiny: The Taken King Walkthrough and Guide if you need to switch gears.