Now it isn't only Hunters who get a chance to sneak.
Now you have Rasputin’s cloaking tech, you have to return to the Moon and fill the crystal with Crota’s soul. Start by running across the bridge from the end of the Lamp section of Crota’s End.
When you appear on the other side, you’ll automatically cloak.
Walk out onto the bridge from Crota’s End. You’ll see a bunch of Swordbearers, an Ogre, Wizards and whatever else. You have to cross to the other side without being spotted. They can smell you, so don’t get too close.
Pick up the Relic, run to the bridge and form it. Just run straight across and into the doors on the other side. Run down the corridor, drop down the hole and you’ll see the area where you killed Crota in the raid.
Run up to the Deathsingers and grab the essence of Crota’s soul.
Once you pick it up, you’ll be exposed to the Taken. Kill everything until Eris teleports you out and the mission ends.