Fly using the Pelican and head to the first tower. Destroy all enemy fliers in the area then land near the entrance. Disembark from the Pelican and continue on foot.
Activate the main core to enable the three attenuators. Then, you have to clear the enemies guarding them and destroy them all. Take note that after destroying each attenuators, more enemies will appear. Thankfully, there should be bunch of Covenant and Promethean weapons lying around.
After destroying all three targets, head out and return to the Pelican. Resupply as needed then ride it. Make your way to the second tower. Like before, you have to take out enemy fliers near the entrance before landing. Head inside and find the controls of the gondola.
As soon as the gondola stops halfway, go to the lower level of the gondola and cross the light bridge. Fight your way through the controls in the topmost level. After activating it, don't worry if it starts to move; it will create a new lightbridge that you can cross in the other side. Just be careful since elite promethean knights will make an appearance as well. You also need to clear the enemies in your gondola as well. Upon returning there, you have to reactivate the whole thing gain.
You won't be able to rest that long since the gondola will stop again. Like before, disembark, clear the next area and reactivate the controls. Once done, return to the gondola and head to the generator. Find the ramp behind and just step into the light to make it overload. Your shield and skill will reset so take cover as the enemy drones appear. Destroy them all then return to the gondola and activate it. Return to the Pelican and leave the tower.
Fly a bit until Cortana gives you a new waypoint. Land there and enter the tower. Ride the current up then proceed. DO NOT run along the pathway as the Didact will alter the tower. If you ever mess up and the game saved as soon as the floor crumbles down, you'll have no choice but to restart the last checkpoint. To do this, return to the main menu, choose the chapter then select the checkpoint you want to load. (If you have a jet pack equipped, then you may escape that predicament) From this point on, it should be straightforward. Fight your way through groups of enemies. When you reach the objective point, there will be two hunters guarding the path. To get an achievement, you must lure one of them near the edge of the platform and make it charge towards you. Get out of the way; if done correctly, the hunter should fall to his demise. (refer to the video below for more information) Defeat them then ride the blue beam up to the tower.
Tricked to fall
In the next area, there are several banshees patrolling the area, not to mention plasma turrets on strategic locations. You can clear them by foot but if you want to make it easier, you can pilot any of the parked banshees in the platforms.
Owning the sky
Make your way to the objective point and go past the door. Continue to the tower controls and insert Cortana there. Pick her up after her attempt then jump from the ledge to trigger a scene.