“Cayde-6's stealth drive awaits inside the colony ship. Find a way to the top.”
You will be able to reach the Colony Ship easily now. Fall off to the right of the backup power source. There is a platform you can easily land on nearby.
After that, you can drop into a hole which will deposit you just in front of the terminal you started from.
Look over the bridge. Be sure to wait a minute after it gets in position. This is because the bridge will collapse some on you. If you are on it, there will be a lot of jumping involved. If you wait, then you know what form the collapse takes and can easily jump across it.
When you enter the ship, more Taken will appear. You need to quickly clear out the Taken Thralls and Vandals. Avoid the Vandals by heading to the left. This blocks their line of fire but does nothing against the Thralls. Eliminate the Thralls from here then deal with the Vandals. Start up the slope opposite the entrance after you have dealt with most of the enemies. Look to the left as you ascend to find another Taken Vandal. Pick it off and then continue upwards.
At the top of this slope, turn to the left. Go to the end of the broken sheet of metal. Jump from there onto the tank and then up to the ledge above it. Cross over to the far side.
Just across a small gap is the door you need to go through next. Jump over to it and head over to the left. There is a Taken Phalanx just inside the door. This thing can easily catch you off guard. Take it out with shots to the legs or head if you are a quickdraw. From there start over to the right through the hallway in front of you. There is a Taken Knight a bit farther in. It is backed up by a Taken Psion. Eliminate the Psion then the Knight to ensure smooth progress forward. Just around the next corner is a Taken Vandal. Sight it and eliminate it.
Jump up onto the collapsed walkway in front of you. Turn to the left. You will find a Vandal on the next landing with a Wire Rifle ready to start sniping at you. Kill him then head to where he was. You have deal with more Fallen just across on next platform. Pick them off or simply jump over there and engage in close quarters. Head up the next set of stairs and you have a pair of Vandals and a Captain.
Take out those Fallen and then jump onto the top of the wall behind them. Once you land on top, duck and turn to the left. Go over to the wall then turn right. Follow the narrow beam in front of you to its end. Turn to the left and continue on the next beam. Head to the end then turn to the right.
Cross over to the next ledge. As you land, look ahead, you have 2 Taken Phalanx to deal with. Just past them are more Fallen. Quickly kill the Phalanx because their shield blast can easily knock you off the Colony ship and you will need to climb back up from the bridge. Jump over the beam or slide under it to encounter a trio of Shanks. Past them is another pair of Taken Phalanx fighting more Fallen. Defeat all of them then go through the next door on the right. Follow the corridor to the right and continue upwards.
The next room has a number of Vandals and Dreg waiting. In the back is a Captain. Clear them out then climb up onto the ledge above. Deal with the remaining Fallen and press forward, going over to the right.
You will find a lift field that will carry you the rest of the way up. Take a moment to reload and stock up. The boss of this level is coming up next. When you land at the top of the lift, there are a few Vandals, Dreg and a Captain. Before you can do much, the next part begins.