Time to start fighting. Head over to the left from the door (facing the door). You will see a number of Taken Goblins begin to emerge. Defeat those you can as they emerge. Be mindful because there are Taken Captains that will be coming up behind you as well. Keep on the move as you fire to avoid getting ambushed too suddenly. Move carefully because of the number of taken. You have at least 3 Taken Captains in this wave to deal with. Clear them out to trigger the second wave.
The second wave has Taken Cabal for you to deal with along with Taken Fallen. Focus on taking out the Taken Centurions only after you clear out some of the Taken Vandals. Area effects to quickly defeat the groups are recommended for this reason. If they get their barrier up, you need to move in close and attack them within the barrier. Remember the Vandals can also act as Snipers. If you encounter any of those, kill them immediately! They pose enough danger on their own.
The third wave is facing yet more Taken Vex. This time though, you will need to deal with the Taken Minotaurs. This is in addition to a few Taken Captains running around the area as well. Clear out what Goblins you can first of any group. After that, focus on the Minotaurs and then the Captains. Fight through and survive to advance.