At the start, turn left and jump onto the left railing and do a slide jump off the right side of the railing once you reach the end of it. Head into the interior of the building.
In the center of the room will be a staircase. Jump onto the railing on the right side. It is possible to do a grenade jump up to the platform on the right which leads to the next area. The grenade jump saves a fraction of second. Regardless of whether or not you are doing the grenade jump, you can jump up to the right platform once you are about halfway up the railing. Walk through the door to the next area.
In this area, there are two possible options. The first option is to head towards the door to the next area by walking between the pillars and doing a slide jump off of the staircase or its railing to boost yourself to the door. The second option is about three seconds faster at best, but it's a bit harder. Instead of walking between the pillars, head towards the right side of the right pillar. You will see a gray barrel in a square on the floor. There is a square diagonal from the barrel that is closer to the door. Stand at the corner of that square that is closest to the door, look straight down, and crouch. Throw a frag grenade under your feet, immediately uncrouch, and jump so that you land just on the far side of the orange cone. Jump as the grenade goes off and you will be launched towards the door. Enter the next area.
In the next area after exiting the set of doors, immediately take a left and jump onto the gray box and onto the middle platform. Bounce a frag grenade off the wall on your left to grenade jump up to the highest platform. Head towards the next door while avoiding being blocked by enemies.
The room with the dead Covenant and marines has some extra ammo to pick up. The middle desk area will have more sniper rifle ammo that you should pick up, as well as a health pack if you need it. On the far side of the room in the center will be a dead brute. Pick up his spike grenade and exit the room. Once outside, make a direct path to the door on the left and proceed to the next area.
Immediately turn left after going through the set of doors and head towards the staircase. Once you reach the very top step, throw a spike grenade at the fusion coil, then quickly run to the other side of it and jump as the grenade explodes. This will boost you onto the top platform. Walk towards the door and snipe and Brutes that get in your way. Once inside, jump off the platform and slide jump off the staircase and snipe any grunts in the way. Exit the building.
Upon exiting the building, use your pistol to kill the Jackal and the Grunt. Jump onto the left rail and jump towards the slanted piece of the lower platform to do a slide jump. Swap your pistol for the fuel rod gun. Jump down to the crane and start sniping enemies. To the left, there will be a Brute, two Jackals, and a Grunt, as well as a Brute on the far side of the platform. To the right, there will be a Brute and two Grunts. Snipe all of these enemies while walking down the crane. Once you reach the end of the crane, make your way to the platform with the Pelican on it to start the wave fight.
You will need to shoot down the Phantoms to progress the fight faster along with the Banshees. The Phantoms that deploy enemies don't get shot down. There are Missile Pods littered around the Pelican and two that are mounted. Only take them off once the Phantoms that come out from the same side are eliminated. Phantoms have three spawn points and randomly spawn each time the level is played. Banshees also assist the Phantoms and the Spartan laser will come in handy if one is too far out for the Missile Pod. The Spartan Laser is useless against Phantoms, but six shots from the Missile Pod will work when hit at one of their 'eyes'. Once the three sets of Phantoms are destroyed, one last Phantom flies from the bottom, take a Missile Pod and shoot it 2-4 times. Once it has set up its spot, rocket the eyes and Buck should say "Jet packs!". If he doesn't and the Phantom is destroyed, the game softlocks. Head up top to end the level.