At the end of my assault on the Cerberus Headquarters I unfortunately didn't meet the Illusive Man in person so that I could put a bullet in his brain. He left his assassin Kai Leng though to deal with me.
I have to say, compared to him the Reapers are just pushovers, I'm having a hard time even just surviving long enough to scratch his shields. His shields can take an enormous amount of punishment, and when I finally got them down once his health bar didn't seem to move at all. Shortly afterwards he had his shields up again, came to close to me and just killed me.
So, how do I defeat Kai Leng?
Best Answer
I'll provide a rundown of how I did this, as a Vanguard on Insanity difficulty. So, expect some bits to be highly specific, with some more general advice thrown in as well.
Your Squad
EDI - She's required for this, so you'll have her anyway. Most important for this fight will probably be Overload. Probably best to spec this for maximum single target damage rather than affecting multiple enemies.
Liara - Since I play a biotic, I bring Liara to set up detonation combos, which is how I deal with trash. Garrus would probably be better for direct boss damage, with his heavier weapons and another Overload, but that might make trash clearing a bit more difficult. I haven't tried with Garrus, though - so that's just speculation.
Mental Prep
It helps to think of the fight in two stages:
Times when you're fighting Kai Leng.
Times when Kai Leng is regenerating, and you're fighting Cerberus troops.
The fight will alternate between these two stages until it's over. Each time Kai Leng regenerates, he blows up a bit of the floor, giving you some pits to take cover in.
The Fight
Right off the bat, Kai will charge. Initially I would charge him, but found it better to let him close, then do the Quick Time Event to fight him off, as this puts a little more distance between you. As Tricause notes below, mash the melee button to fight him off.
Cast Overload on pretty much every cooldown.
Charge him. This sounds counter intuitive, but after many failed attempts using a Mattock/SMG, charging him and just blasting away with a shotgun proved most effective. Play to your strengths. Every time you charge, you can line up some decent shots, and get a shield boost.
When Kai blows up the floor, he'll run to the same spots every time. Learn these, and back off when he does. He'll recharge his shields as he does this, so shooting him is more or less a waste at this point. Back off, get into cover if you can. As he does this, some Cerberus baddies will drop in. Here is where I would use Shockwave/Pull and Singularity/Warp in various combinations to clear out these guys. Maybe throw in an Incinerate from EDI since it won't really affect Kai during this time. (Side note - I had EDI specced for the chain overload, where it affects multiple targets, so I was able to zap Kai a little bit if I needed to deal with a Centurion, but I'm not sure how much it helped).
This is basically the entire fight. Slowly but surely you'll whittle down Kai's shields. For me, it seemed that the fight was over before I got him to zero HP, but I can't be 100% sure. If you just think of the fight in terms of stages, rather than looking at his health bar, it becomes much easier and goes much quicker.