After they die, search the body of Shaela, the last of the Jedi terentatek hunters, to pick up her journal and the best lightsaber crystal in the game. Assuming you're a Light side player, you'll want to implant this into your saber as soon as possible. At any rate, you'll need to pull the lever nearby to access the antechamber here, which contains two special grenades.
Take the grenades and head south from the corridor branch. You'll encounter a pool of acid, and will have to decide which grenade to throw in. Since the fire grenade makes the acid airborne and kills you, you might want to use the ice grenade, which freezes the pool and makes it passable.
Walk over the pool and head towards the door; there's a deadly plasma mine that can dish out up to 70 damage to you if you don't spot it, so make sure you're healed up before passing through. Grab the Star Map and the Sith lightsaber, then walk back down to the acid pool for your final test. Go through the same preparations as you did for your fight with Malak: good energy shields, mind-affecting immunity if possible, increased will and fortitude saves, etc.
Uthar and Yuthura wait for you, and this is where all the scheming in the Double-Cross quest will pay off. Your choices are: help Yuthara defeat Uthar; help Uthar defeat Yuthara; or attempt to take both of them on. If you accomplished any of the outcomes of the Double-Cross quests, you'll reap the fruits of your labor here, as one of or both of the competitors will be weakened by poison. Even so, a Dark Jedi of these levels of power is no powder puff.
If you side with Yuthara against Uthar, he will feel the effects of the poison if you placed it in his bed earlier, then both you and Yuthara will be attacked. Uthar is the more difficult of the two, if only because his death field attack will heal him repeatedly just when you think you're about to finish him off. When he runs out of Force points, he'll activate a life support kit; this is when you know you're almost through with him. After he dies, Yuthara will turn on you, and again, if you poisoned her, she'll feel it now. She's a much easier foe than Uthar.
If you choose to stand against Yuthara, you'll take a Dark side hit if you inquired about her past back in the Sith Academy. As stated above, she's not too difficult to defeat. Uthar will subsequently turn on you afterwards, though, unless you displayed a foolish degree of loyalty by following through the Double-Double-Cross quest without informing Yuthara of your plans, and without poisoning him as well. If you did poison him, or if you did tip off Yuthara, you'll have to face Uthar alone, which is obviously a tall order.
Low-yield thermonuclear devices will come in handy when taking on Uthar and Yuthara.
Facing Uthar and Yuthara together is obviously going to be difficult for any but the brawniest of Jedi guardians. For once, you might want to dispose of the weaker enemy first and kill Yuthara before Uthar, if only to prevent your energy shield from falling as quickly, and since Uthar will abuse his death field attack to stay alive much longer than he should be able to. If you're interested in a less complicated method of proceeding with this attack, just place as many mines as you have in the corridor leading down to the acid pool; once the pair attack you, run away from them, and when they hit the mines, they should be crippled, if not killed outright. Note that if you do pursue this course, and actually manage to kill both of the Dark Jedi, you'll have to fight your way through the entire student body of the Academy on your way out. You'll regain your teammates once you reach the Academy's interior, though, so this shouldn't be too hard for you; if you're looking for extra experience, or if you just want to be the king of the hill, this is the way to go.
Uthar's body contains 3,000 credits, a Cinnagar war suit, and a security domination interface, while Yuthara's contains just a poison grenade, a hyper-adrenal alacrity stim, and 1,500 credits.