From Halopedia, the Halo wiki
Okay, so; you've joined up with the forces of the UNSC Infinity and managed to drive of the Didact. So, now, what's next? Simple; you need to get Infinity OUT of Requiem, and to do that, you need to take out the gravity well that sucked her in and is keeping her there. Easy enough job, right? Not so much...there's four particle cannons guarding the well. If Infinity gets too close, she's toast. They need to be taken offline. That, of course, is where you come in.
Meh, Size Isn't Everything. You Need Firepower Too.
The level begins as you step off a Pelican, armed with a Battle Rifle and an Assault Rifle. The path ahead is pretty clear; there's several very honored Marines standing where you need to go. Walk past and enjoy the thrill of being saluted. Commander Palmer will comment on you being here, and then you'll get your first glimpse of the machine you will ride; the Mammoth. This rolling death machine is everything a Spartan could want in a vehicle. Aside from being awesome to look at, she's armed to the teeth with twin rocket turrets, and her insides are practically bursting with small arms and several Warthogs.
Mount up through the side, grabbing any weapons you fancy from the racks inside (They're on the second level, towards the front of the bay) and meet Commander Lasky at the front. He'll give you all the details you need to know about the upcoming mission. Once he's finished, the Mammoth will start rolling. Palmer mentions that there are jetpacks aboard and suggests you get one. This is sound advice; do so. A waypoint will point you where they are. On the same level, towards the front of the Mammoth, are sniper rifles. Save these for later.
Once you have your jetpack, mount up the port (that's "left", facing the front of the Mammoth for you non-nautical gamers out there) rocket turret and shake your head at the first attempt to take out the particular cannons. Almost as soon as it ends, you'll come across a small group of Covenant infantry dug into the hills. Don't use your personal ammo on them; blow them to chunks with your turret. Prioritize the sentry tower and the Shade first; these are your biggest threats.
Once you are past the Covenant, you'll come across the remains of the last unlucky Pelican from the failed attack on the cannons. She's still mostly intact, and, more importantly, her cargo of a Target Designator (marked by a waypoint) is still in one piece too. The Designator is what you need; with it, you can use the Mammoth's mini-MAC to obliterate the cannons safely from the ground. Of course, first you have to get it. And in your way are several batches of Covenant, including some Ghosts and (a few moments after you show up) a Wraith.
The easiest way to deal with this whole section is to fight fire with fire; climb down into the Mammoth's main bay and mount up one of the Warthogs there. Load her up with Marines (or a Spartan-IV or two) and roll around till everything's paste. Of course, in typical Halo sandbox fashion, this is not the ONLY way to do it. You can go on foot if you want, hijack a Ghost, grab the snipers from the Mammoth and pick things off (not recommended but completely doable)...the list goes on.
Anyway you go about it, the area should be completely clear of Covenant by the time you're done. Hurry over to the Target Designator and walk over it to equip it.
Your first target to obliterate is not, as you'd expect, the cannon, but rather the Phantom's flying around peppering the area with plasma cannon shots. Let them taste hypersonic UNSC steel and relish as they come apart. Then turn your fury to the cannon. Light her up with the Designator, and watch as the cannon lights it up. The moment the particle cannon comes apart, the Mammoth will start rolling again. Thankfully, it moves slowly enough that you can easily hop aboard again. Or, if you want to be completely sure not to miss it, climb aboard before destroying the cannon (an added bonus; you get to see the MAC fire over your head before obliterating the cannon).
Okay, Okay, You Win
The next part of your ride is relatively peaceful. Take the time to reload any ordnance you might have expended. Then climb to the top deck of the Mammoth and get ready for some Phantoms to come in. Use the Target Designator to blast them apart. The MAC reloads at a ridiculously slow rate however, so don't be surprised if one Phantom starts to move off before you can fire on it. Don't worry about it; its Plasma cannons can't hope to stop the Mammoth. Simply find cover until the MACs back up, and if it escapes...well, Infinity's overhead. Its not your problem anymore.
What CAN stop the Mammoth, however (or at least slow her down) are the next obstacles in your path; a trio of shield generators. These ones you can't hit with the MAC sadly; you'll need to deal with them manually.
Once again, this process is open ended. Grabbing a Warthog from inside and riding out in it is recommended however, as several Ghosts and even a few Wraiths will come looking to crash the party. No matter how you go about it, the result should be several very destroyed shield generators and quite a lot of dead Covenant. As soon as the last one's down, remount the Mammoth.
The next particle cannon is directly ahead. As soon as you have line of sight on it, blast it with the Target Designator. The Covenant won't take to kindly to you busting up their bosses toys...as soon as Lasky shouts about an "unidentified contact", get ready to take cover.
The massive flying vehicle that opens up on the Mammoth is called a Lich, and it's pretty much a flying Scarab. And as if it weren't enough, the Mammoth will also be besieged by a myriad of Covenant ground vehicles.
Hey, I Just Got This Thing!
Take out your rage at the damage to your ride by using the rocket turrets against the ground vehicles. In addition to that, sitting peacefully by the cliff edge (and nicely marked with an Ordnance waypoint) is another tool that can help you get revenge; a Gauss Warthog. Mount it up and search around for some Marines to ride with you. If you can't find any, park in a place where you have good line of sight on the enemy and open up.
While you're dealing with the enemy, the Lich will take possition over a near-by mesa and deploy a grav lift. Your job now is to deal with it Halo 3 Scarab style; get inside, smash the power core.
First though, make your job a little easier and remount the Mammoth. She's still alive, and Lasky will roll her forwards a bit, meaning her rocket turrets can get a solid angle on the Covenant milling around the base of the Lich. Grease them all. Once the way is clear, move up to the Lich. There are several ways inside her. Straight up the grav lift is the most obvious, but you can also jetpack up from the rocks underneath for a more stealthy approach. Several S-IVs will follow you and provide fire support.
Once aboard, simply kill everything that isn't human, then head to the back of the Lich. The power core will be marked with a "neutralize" waypoint. Either shoot it or bash it with your armored fist until it explodes. Once it does, follow Cortana's advice and "make an exit"; straight out the side of the Lich. Use your jetpack to slow your decent so you don't take damage (fall damage is back in Halo 4 for some reason), then watch as the mighty machine flies off and dies in a pretty purple fireball.
Once again climb aboard your battered but still proud steed and rearm if necessary. The Mammoth will roll on pleasantly for a bit, giving you time to listen to the radio chatter between Captain Del Rio and several of Infinity's infantry companies, and Cortana a chance to reveal some unpleasant realities about rampancy.
Up ahead is the end of this fun little ride; a massive rockslide that not even the Mammoth can go around. Thankfully, to the left, rising above the rock walls, is the command center for the particle cannons. You're next job is to get in there.
Okay, You Wanna Play Hardball?
Grab whatever ammo you need (and the two Sniper Rifles on the top deck of the Mammoth) and hop down. The path ahead is fairly linear, but there are lots of Covenant (including quite a few Jackal Snipers) and even a few Prometheans guarding your way in. Kill everything in your way, putting the Sniper Rifle to good use until you run out of ammo (several ordnance pods will be deployed by Infinity near the Mammoth's location; one of these holds a third Sniper Rifle you can reload your current one with). Once you run out of Sniper rounds, grab a Beam Rifle off a dead Jackal and continue to use it the same way.
Your path will lead you to a large, three-leveled structure crawling with Covenant. Use your precision weapon to pick off every enemy you see before moving forwards. If you run out of ammo, there are several full Beam Rifles in crates near the bridge leading to the structure. Once you have cleared it, move onto and up it, finishing off everything you find. Once its clear and you're sure you won't get shot in the back, move forwards once more. Promethean Crawlers and Knights will appear, backed up by a few Watchers. Deal with them and move forwards more until you reach the "back wall" of the canyon you are in. This final structure is crawling with both Covenant AND Promethean forces. Show no mercy to either, grab any ammo you can, then enter the waypoint-marked door.
Inside, follow the tunnel to the first large room. There, a single Sentinel awaits you. Don't worry about it; it won't open fire upon you. It is merely a guide. Approach it to have the door before you shut and the proper one open and lead you to an elevator. Ride it down, then move through the door straight ahead (the one on the left will close before you can reach it). Once through that one, hang a right, towards the Sentinel and move through the door to the platform at the other end of the massive room. Insert Cortana into it to have her deal with the remaining cannons.
Once she's through, and her strange little moment has passed, run back out the way you came, but take a right, across the glowing light bridge that will open for you. Follow the corridors till you reach a large room and trigger a cutscene that reveals some interesting facts about humans and Forerunners (which will, sadly, be quite well known to anyone who's read the books...)
Following the end of the cutscene, your peaceful little interlude comes to an end as several Crawlers come charging for you. Ignore Cortana's calls for you (she's quite safe where she is) and put down the Crawlers and the Knights that show up moments later before retrieving her. With your AI now in hand, move through the open door to the elevator and ride it down. You need to get back outside; the fight isn't over yet...the gravity well needed to be eliminated. Jump through the portal at the end and get ready for some old-fashioned UNSC ground-vehicle ass kicking.
I Was In The Neighbourhood. Thought You Might Need A Hand.
Upon your exit from the portal, you find yourself in the midst of a ground battle between a UNSC armor division and several Covenant Wraiths with the soothing, sultry tones of Gunner Sergeant Stacker in your ear. There's a Scorpion near by; commander it and put it to use against the Wraiths while the situation is explained to you. Once the first area is clear, move ahead, blasting the hell out of any Covenant stupid enough to get in your way. Stacker will call out when you're clear. As you clear the third line of enemy armor, you will run into yet another shield wall. The generators are to the left; roll up and obliterate them by any means necessary. The 90mm cannon of the Scorpion does a rather good job of it. Just be careful not to blow yourself up by firing to close. Once the generators are down, climb out of your tank, sprint ahead, and use the dropped Target Designator to unleash hell in the form of 90mms of explosive ordnance on the gravity well.
Nicely done Spartan. Your way home is clear...or is it?