Once out of your pod, head straight across the bridge to this room. You can scan weapon systems here with this terminal if you want, but it's not required.
Leave the room through the door on the right, and head up the ramp into this room. Take a left in here.
Run through this room, then take a left again and go up some stairs.
These corridors are pretty straightforward, allowing you to focus mainly on Chief's conversation with Cortana. Head left through the open door into the room you see beyond the glass here.
Walk up to this machine, and...weren't expecting that, huh? Don't worry, makes me jump too every time. :P Head out the door that just opened up behind the console and take a right down a ramp.
Keep following the corridor straight ahead until you get to these elevator doors. Open them by tapping the indicated button repeatedly until...
Whoops. Should've listened to Cortana.
This won't stop the Chief of course! Keep pressing foward while Chief slowly makes his way up the shaft.
Eventually some debris will begin falling on you. Chief will quickly glance to the left or right. When he does this, move the thumbstick in that direction to make him jump in the direction he just glanced in. Repeat this until...
Huzzah! Solid ground!
...well that was quick. Press the B button when prompted and he's history. So much for that whole "truce" thing.
After that bit of excitement, follow the corridor again until you get to this door. Ahead you'll see some stairs, with an Elite beyond them.
Crouch and sneak up behind him slowly, then...
BAM! The best strategy is to just tap the B button behind him to silently assassinate him. If you wanna be hot stuff though (like I chose to do), hold the B button for a second and you'll stab him in the back and throw him down. Awesome!
After taking down the Elite, you should be able to mop up the rest of the Grunts in the room pretty easily.
After taking care of them, head back up the stairs where you killed the Elite, and use the console to override the blast shields.
Whoops. That's a problem.
Landing craft will attach to the ship, and some Grunts and two Elites will come storming out. Do what Chief does best and take them down.
Our next objective is to get to a missile launcher on the ship. Follow the objective marker to these doors.
Wait for a few moments for the airlock to cycle, then head left through this room.
Follow the corridor to this door, and...
Surprise! Take these guys down real quick.
Continue on down the corridor to this door. It opens to reveal...
Again?! These guys aren't a challenge though.
Head to your right and down the stairs.
At the bottom, an Elite and a few Grunts will start shooting at you. Make short work of them.
Go through either one of the doorways and follow this path to...
More Grunts, two Jackals and an Elite! Yay!
When they're dead, head through the open door behind their bodies and take a left.
Inside this room, you'll see Grunts, Jackals, and three Elites. Have fun!
When they're all taken care of, circle the perimeter of the room until you find this doorway.
Head through and take a left.
Walk through this door and follow the corridor until...
Space! Yay! Your objective will be across the way on a raised platform.
Before you head over there, go to your right and pick up some Battle Rifles. You'll thank me.
Fight your way through Grunts, Jackals and Elites to get to the missile controls. Watch out for these Jackal snipers on the ledges. This is where your BR comes in handy!
Head up this ramp. It's directly below the ledge that houses the controls.
Surprise! Jackals and an Elite!
When they're dead, use the missile control console aaaand...
Well that was anti-climactic. Head back down the ramp, go back to the BR ammo and refill if you need to, and start heading toward the missile door.
A troop transport will drop off some Jackals, Grunts, and Elites. Because your job was already too easy, right?
You can fight through them, or you can be a sneaky devil like I was. Run back to the BR ammo, then turn and face your objective like this.
You can run and gun straight through like a madman like I did and reach the missile door without much trouble. Trigger the magnetic accelerator when prompted.
...or not. Run back to the door you entered this huge area from! It's marked with an objective marker.
Wait a moment for the airlock to cycle and then run through the door.
Take a left and continue down the corridor. A large piece of the ceiling will fall and block your path, forcing you to go through the door to the right.
Take another right, and...
Ouch. Drop down the hole and head straight up those stairs.
Keep running and following the objective markers!
That's it, you escaped! Enjoy the cutscene as Chief's newest adventure begins.