From Halopedia, the Halo wiki
The Devil His Due (Mission Start)
You start out at mid-health and armed with only a single M6G magnum. Don't worry about conserving ammo; there's more pistols later on and you'll be discarding it soon anyway. The area you start in has no enemies; just a bunch of dead civilians so run on ahead until you pass through the dark room with the broken door.
As you exit, you'll come to some stairs where three Skirmishers are on patrol. It's easiest to headshot when they're crossing from left to right. Hit one, and the others will shoot at you for a while before running away. It pays to kill them now, since otherwise they'll turn up later to harass you. Once they're gone, head up the stairs, where you'll find a dead trooper with a pistol. It only has a little ammo, but it's enough to recover any you lost. There is also a health pack nearby. Heal up and head into the next set of doors.
I Just Want To Hug You To Death
As you enter the doorway you will hear over the radio reports of Covenant suicide squads. There are three Grunts that will go kamikaze and rush towards you. Finish them from a distance with a quick headshot. Turn on your night vision and head to the stairs leading to the dark corridors of the city. There are two more Grunts that will try to blue ball you; one at the bottom of the stairs and one around the corner. Keep your distance and take them out same as before with a headshot from your Magnum. As you turn the corner, there is an Armor Lock you can swap out your Sprint for. You may also want to go back and pick up a Needler to collect ammo for later in the mission. Keep your Magnum handy for easy headshots. Tip: Keep an eye on your radar and listen for the suicide cries of the Grunts that rush you.
The next section is really close quarters combat. At the bottom of the next set of stairs around the corner are three more Grunts who are literally quite startled to see you. Quickly back up the stairs and repeat your tactics. A safe distance and a headshot to finish them off. If you have Armor Lock equipped, you can activate it if the Grunts get too close for comfort. Once they're dead, carefully proceed to the next area but don't go too far as there are more kamikaze Grunts ready to kill you. Lure them out by triggering them to rush you. Watch your radar and listen for their pitiful cries as they attack. Again, keep a safe distance and eliminate them quickly with a headshot. In some cases, they may trigger an explosive chain reaction that will wipe most of them out.
Once everything is quiet again carefully proceed to the next area. There is Magnum ammo near a dead marine by the elevator doors. Be careful! There is a pit of doom here with some railing missing on some of the bridges. Cross safely and head to the last area. There are multiple Grunts on the level above you and attempt to suicide rush you. You know the drill by now. Safe distance; headshot; and most likely a big chain explosion. If you didn't kill all the Skirmishers in the first encounter, they will be here to pester you. Eliminate them. When every alien is dead it's time to get back to daylight. Climb the stairs and head to the exit. There is a health pack on the wall here if you need it. If you picked up a Needler earlier, you should have a maximum of 96 rounds which is handy in the next section.
Brutes. Even Jackals Don't Like Them
Exit out the door and a Spirit will pop up with a pack full of Brutes. Ignore them and head left quickly down the stairs and kill the Brute harassing a civilian. If you are quick enough you can sneak up behind him and land an assassination. Alternatively: you can use your Magnum or a Needler if you have one to kill him. As you link up with UNSC forces, kill the next Brute ahead of you as they "play" with the civilian. The Spirit will drop off three additional Brutes and another one is in the back near the food kiosk pestering another civilian. The Needler really shines in this section as it only takes 6 needles to supercombine on a non shielded target. Once they are all dead, a door will open and an additional Brute with three Skirmishers will emerge. Take them out. A well placed frag thrown at the door can yield good results as well. With all enemies in the area dead, head back the way you came and go up to the upper level. There is some Sprint you can swap out and a Sniper Rifle! You will be needing this in next area and throughout the end of the mission. Once your set, head to the atrium doors to the west.
As you enter the atrium entrance, head up the stairs to the left. There is usually one or two Grunts here. Melee them. Turn right and head into the main atrium section. There are multiple Brutes, Grunts, and Jackals in this area. They tend to move around the atrium so keep an eye out for enemies close to you. The Brutes are your main enemy to concentrate on. Eliminate them all with headshots, Needler supercombines, ect. There is also a Brute Captain on the upper tier with a Concussion Rifle. If you picked up the Sniper Rifle earlier, drill him with a headshot. There is also a DMR on the top near a planter and one near an ammo case on the bottom floor to the left you can swap out your Magnum for. Clear out all the rest of the enemy forces and head to the elevator at the back. Before pressing the button to call the elevator, take note of the weapons in the area. There is a crate with additional Needler ammo if you need it and a few Magnum rounds near by. If you didn't grab the Sniper Rifle go back and get it. Grab whatever you feel suit to kill Covenant with and activate the button.
Why Is There Only One Elevator?
After you hit the button, two Phantoms will fly in to drop off reinforcements in the upper and lower courtyards. The lower courtyard consists of a pair of Brutes, some Skirmishers, and a Brute Captain wielding a Gravity Hammer. The Upper courtyard consists of an additional pair of Brutes, a group of Grunts, and another Brute Captain with a Hammer. This guide will start with the latter as you are close and have a elevation advantage over the enemies entering in the lower part of the atrium. The Sniper Rifle is key here. Note: If you are not adept to sniping you can use the DMR and the Needler to take out enemies as previously mentioned.
As the Phantom lands in the upper courtyard, take out your Sniper Rifle and wait for the pair of Brutes to get out. Drill them with a headshot. Kill the group of Grunts next with a well placed grenade or headshot them with the DMR or Magnum. Immediately switch back to your Sniper Rifle and snipe the Captain as he gets out. Once the upper courtyard is clear, move to focus on the lower courtyard invaders. Mind the Skirmishers and focus on the Brutes. Kill the Brute pair and nail the Captain with some sniper headshots. Clean up the area by eliminating all the Skirmishers and head to the elevator.
Too Close To The Sun (Rally Point Alpha)
Welcome To The Bullfrogs
After exiting the elevator head to the outside where the ODST’s (aka The Bullfrogs) are engaging in fighting some Banshees. There is a DMR crate to your left (which also contains a shotgun) and one of the ODST’s has a Rocket Launcher you could swap out for. The choice is yours. Watch your footing and head to the right to the gates that contain the jetpack and equip it.
There are multiple routes through the next area and it will be up to you how you want to fight the Covenant forces. A good tactical advantage is to pick off the enemies from afar with the DMR and/or Sniper Rifle.
The main area consists of about 4 levels of game play. On the lower level is some Grunts and Jackals, but watch out! One Grunt has a Fuel Rod Gun and will ruin your day. Make him priority one. The second level will have a pack of brutes that will aid the Jackals. You can pick the brutes off with some head shots with the DMR or you can get cozy with a Needler and detonate them. Wipe them out. Keep a heads up as Brute Captain with a Gravity hammer will drop down to join his pack brothers to slay you. Kill him too. Remember you have a Jetpack and if the Captain or any enemy gets to close, you can fly up out of the way. The third level will have a few more grunts and the fourth level will have a few more Brutes and another captain with a Concussion Rifle. The captain is the most dangerous, especially on Legendary difficulty, as the concussion rifle will devastate your shields and health. Once every enemy is dead, head to the stairs to the west near the back and head to the next area. As you enter the open lobby, turn around and jetpack up to the next set of doors.
The Corporate Park
As you enter the corporate park, a group of Marines will be taking cover with civilians from a Phantom dropping off some Jackal reinforcements. There is an ammo crate nearby with additional DMR ammo and a Rocket Launcher. Again, you can either take the rockets of give them to one of your allies to use. The latter may help it easier to clear the Covenant ahead of you. Mind the Phantom and take your DMR and look across the open chasm for the Jackal Sniper with a Focus Rifle. Pick him off now, or he'll harass you later. Help the Marines clear the courtyard of some Grunts and take care of the Jackals that were just dropped off. Before you go to the next area, you should get to higher ground. There will be a balcony overlooking the next area with additional DMR ammo and another Sniper Rifle will be here as well. There is also a health pack if you need it.
This next area is somewhat of a shooting gallery as you can eliminate enemies across the way. However they can shoot at you too so take cover when needed! There will be some more Grunts, Jackals, two Brute Captains and another Jackal Sniper with a Focus Rifle. Kill him first otherwise he'll annoy you stripping your shields. Clear out the cannon fodder and use a head shot capable weapon on the two Captains. Once clear, cross the bridge and keep moving up. A good strategy is to hang a left at the stairs after the bridge and go West up a ramp to the level the Marines are standing on. This will trigger a checkpoint but will also trigger another Captain wielding a Hammer. This Brute is thirsty for blood and will kill everything in his path. Hang back and use your Sniper Rifle to nail him dead but be careful of your allies and the civilians when you do this.
Before you join the rest of your allies at the big stairs, you should note that at the very top of the level you need to get to, there will be a Captain with a Concussion Rifle. On Legendary difficulty, this will be a Brute Chieftain. Take cover quick and use your sniper rifle to kill the nasty Brute up top. Note: He tends to hide around up there so be patient with locating him. Climb the long stairs (or jetpack) up and kill the small group of Grunts here. There is some ammo in an upper balcony above some bathrooms to your northwest you can use. Eliminate every alien and head east to the landing pad.
The Landing Pad
I Should Have Become a Watchmaker (Rally Point Bravo)