“Let your Ghost scan the area to locate a backup power source so you can extend the bridge to the colony ship.”
At the top of the elevator, you will find the bridge that Cadye had to get working again has been moved. It is explained that the Fallen liked did this to get the Taken to break pursuit. You need to restore power to the bridge to move forward. If you summon your Ghost, you will see the terminal will light up and you can see a power cable leading upwards. Turn to the right of the console and look for the stairs leading up.
Head up the stairs and go over to the right. Go around to the far side of the center of the tower. Look to the right again to find the next set of stairs leading up. Just head up the next set of stairs after that. Head to the right and take the third set of stairs upwards. On this landing, go forward and to the left. You will see a machine with a blue tarp on it. Jump up onto the machine and then up onto the platform above.
Continue upwards to reach the backup power source. A Devils' Spire Dead Ghost is located on the tallest antenna nearby at the top.