Rampant
Objective: Find Cortana

This level...is very...very annoying. Throughout the level, you will encounter an army of all Flood-types along with
numerous apparition-like vision thingies from Gravemind and Cortana.

So, once Master Chief has the bright idea to leave his Banshee behind to where he will not be able to get to it again
make your way forward until you reach Cortana...literally.

As you proceed through this level, make sure you have an Energy Sword and a Battle Rifle or a Carbine along with plenty
of grenades.

The first large room you enter (drop down in) is the one you leave in.   So at the end of the level, once you get back to this room, you know you're at the end.

When you enter a room with a purple object sticking out of the ground, jump on it and straight across to get to the doorway to the left.  

Alright, once you reach a large room (the REALLY large room which is later in the level) make your way to the other side across through the middle and enter the door there. Keep going...keep going...keep going until you get to Cortana. Cut scene time.

Nor Hell a Fury
Objective: Escape

Yay. Cortana still has the index from the first Halo game. Now you can finally use this to your advantage.

Go back to the really large room and activate the controls in the center. Now destroy the three reactors (or whatever they are called) that opened up.

Once done, make your way ALL the way back until you reach the second largest room and you'll see the Arbiter to the right fighting some Flood. More to the right is a Pelican, get to that bird and level complete. Jeez...that level was a thriller.