In many cases, the Scarab will approach your location and just continuously start spinning in circles without even opening fire on you. This will allow you to shoot off its back and straight into the core for an easy kill. Otherwise, you'll need to park further back as shown below.
Hide behind the rock and bombard the Scarab with tank shells to kill off the crew. When it gets close to the rock ledge like in the video, disable it by shooting the joints. Then jump it and take it out manually. As soon as that little alarm inside sounds, RUN! That way you can keep the full shields you just received.
Real Men Don't Read Maps
Grab one of the plasma pistols in front of the door. It should have a full battery. Steer clear of Spark as his bluish beam has a tendency to "sting" you too. When the door opens, you'll have to act quickly. Head right and you'll catch a Brute blissfully whizzing on the Forerunner architecture. What nerve! Assassinate him. The Grunts should still be asleep, so tap them out one at a time. Be careful to not knock any bodies into any that are still living.
When the room is clear, head through the door and down the ramps. You will face a similar situation in the next area. Drop down and nab the Grunt waltzing away from you. Then head back upstairs, through the other door, and into the next room. There will be a Brute Captain patrolling the walkway. Make sure he doesn't spot you. As soon as his back is turned, head on over and box him out. Again deal with the scattered sleeping Grunts.
The next segment is where the real action starts. Prime your plasmas and head downstairs. As soon as the door opens, stick the Brute that stands in your way. If you're lucky, you might be able to stick the next one further down. Then back off and let Arbiter and the Marines take over. There will be at least three Brutes remaining (all with Brute Shots) and two pairs of Shielded Jackals. Jump in only when their attention is drawn elsewhere. Combo the Brutes when you have the chance, and headshot any whose armor is destroyed by your allies. If necessary, you can use one of the leftover Jackals to recharge your shields. Just dissipate one's energy shield via the plasma pistol, and assassinate it as it tries to scramble away. Now head out the door and activate the Cartographer. See? I told you the Ark was big.
By shooting the door on the left inside the hall, you can trigger the Brutes to come to you. If you use plasmas to kill them, they won't use their equipment, and at least two of them will be packing regenerators, so just an extra thought when you're choosing how to take 'em out. You will be able to use this method with at least three, but the fourth may decide to grow a brain and stay back. He'll be hiding in the little off-section to the left. Once the first three Brutes are down, ready your plasma pistol and charge into the room. Take heed of the War Chieftain (with a plasma cannon) stationed on the opposite side of the room. Wait until his attention is elsewhere. Once you reach the left side of the room, the remaining Brute will be hiding further down. Kill him with a combo.
Charge him while charging your plasma pistol. When you're close enough, zap him. This will stun him just long enough for you to move behind him and land that assassination.
Now if you didn't deal with the Brute Stalker before, you're in for a real treat. Head downstairs where you'll meet four cloaked Brute Stalkers. The first one will be on the right side. Send a sticky his way, then head through the door downstairs. His buddies will start coming through one at a time. Again it's just easier to lob grenades their way. I prefer firebombs myself as there tends to be less margin of error.
Method #1: Normal
This one doesn't guarantee your safety nearly as much as the others, but it's certainly doable. Go back downstairs, grab a cloaking device, place a few plasma pistols in the "lobby area" just inside from the outdoors, juggle the two regens from before down there while you're at it, and head out onto the platform. I'd also recommend grabbing the War Chieftain's plasma cannon so you can periodically check your health status.
Method #2: Glitched
Special thanks goes out to VincentKurayma for this discovery. This method I deem to be the safest. Picking up from where we left off prior to the first method, jump down from the Cartographer to the platform below. The Hammer Chieftain will already be there, but he won't be able to attack you. Smack him in the back, take his equipment, and head back up into the safety of the lobby. This will trigger the rest of the enemies to spawn. Again stock up on plasma pistols and equipment then deal with the Brutes and Carbine Jackals as mentioned above. Using this method, you'll be able to keep your cloaking and use it later if need be. Plus you don't have to worry about hightailing it off the platform before your cloaking wears off and all hell breaks loose.
Method #3: Kamikaze
And just for fun...