After you destroy the asari statue in the temple, a green VI will emerge. It will quickly reveal itself to be a prothean, and during your conversation with the VI it will claim that it is too late to save your galaxy already. At first, it will be reluctant to tell you the secrets of the Crucible. After some coercion, it will decide that there is no harm in telling you, even if you are all going to die anyway. Before the VI can tell you what you need to know, however, Kai Leng will enter the temple and the VI will retreat inside of itself. A hologram of the Illusive Man will accompany him.
You will have several conversation options with the Illusive Man, but none of them will really accomplish anything. If you choose “Whose side are you on?” you can get a Paragon/Renegade persuade option, which can be helpful if you are trying to max out one side or another. Otherwise, finish the conversation and get ready to fight off Kai Leng.
Boss Battle: Kai Leng
Kai Leng can move from spot to spot relatively quickly thanks to a warp ability, but during actual combat he is surprisingly slow. Equip an Assault Rifle or SMG and retreat towards the back of the arena. Unload on Kai Leng while you allow him to focus his attacks on your squad-mates instead of you. If the boss gets close to you, use powers such as Shockwave, Throw, or Grenade to keep him at bay while you retreat. He might be able to wail on your squad-mates for a while, but Kai Leng can kill you surprisingly quickly if you let him have the chance.
Once you have taken down Kai Leng’s shields, he will retreat to the front of the arena and call in a gunship for cover while he regenerates. Take cover behind one of the rows of chairs as the gunship peppers the temple with machine gun fire. When it leaves, resume your attack against Kai Leng. He will now throw Biotic projectiles your way every once in a while, so be on the lookout for the crescent-shaped attack as it soars towards you, and roll out of the way when it gets too close. Otherwise, simply keep attacking as you have been before, using your squad-mates as distractions while you unload on Kai Leng. After two more times of retreating to power up his shields, Kai Leng will retreat and order the gunship to take out the temple’s support pillars.
Kai Leng will escape with the prothean VI and Thessia will all but die at the corrupting touch of the Reapers. Head back to the Normandy and inform Anderson and the asari councilor that you have failed your mission.