Objectives: Escape the Leviathan
The first two rooms here will contain, respectively, a squad of Sith troopers and a group consisting of two Dark Jedi and a Dark Jedi master. Kill all of them, search the rooms, and proceed through the blast doors to the north. Before heading down the ramp, though, you're going to want to re-equip your main character. Be sure you have the best energy shielding available; the verpine prototype shield that Saul dropped is excellent here. A nerve amplifier belt is the next most important thing; hopefully you haven't sold them all. If you have, you can substitute Darth Bandon's fiber armor; it grants you immunity to mind-affecting attacks as well. If you have an implant slot, use anything that will boost your fortitude saves in it. If you've mastered flurry, you might want to put on the heaviest armor you can equip. Un-equip your other teammates completely.
Save your game at the start of the ensuing battle with Darth Malak; despite your best efforts, you might still die during this duel. Your first action should be to activate one of your shields. Malak generally begins by activating Force immunity, so you'll probably want to stick to your lightsaber with regards to damage-dealing. If you did manage to equip an item that grants you immunity to mind-affecting attacks, his horror power won't affect you, which is a good thing, since a successful hit with it leaves you incapable of movement for a couple of rounds.
Aside from Malak's Force powers, you'll have to deal with his lightsaber attacks. He has a fairly decent attack bonus (+16 base), but if you can get your defense up to around 30, he'll still have a hard time getting through. Even if he does, your energy shield should be enough to keep you alive. Aside from the basics of using cure, heal, or a medpac when you run low on life, you'll want to boost your attacks per round, either through flurry or an upgraded speed power. This might also be a good time to use some of those hyper stimulants you've probably been hoarding.
After you knock Malak's health down to around half of his bar, he'll run off. You'll need to follow him, but you'll have to skirt the main room, which is locked, and enter from the rear door. Another small skirmish follows, but this time Bastila comes to rescue you after you're irrevocably stunned by Malak. Make like a tree and leave through the hangar bay doors.
Once you're free from the Leviathan and have fought off the Sith starfighters, you'll have to have a pep rally with your crew. You'll automatically be whisked away to the planet that you haven't recovered the Star Map from.