How do I defeat Kai Leng in Cerberus Headquarters?

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:

1. Times when you're fighting Kai Leng.

2. 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

1. 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.

2. Cast Overload on pretty much every cooldown.

3. 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.

4. 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).

5. 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.

Bring people with abilities that damage shields (Overload is super effective), respec them if necessary. Use fast-firing weapons and ammo powers that damage shields. Use cover he creates by exploding the floor. Spam grenades.

I managed to get him playing a soldier (level 55) on insanity. I was using a Black Widow and Avenger, both level 5; my armor, intel and skill bonuses were maxed for headshot damage then weapon bonuses. My second squadmate was Garrus (Phaetus & Black Widow).

The first thing I did in the battle was pop and adrenaline rush and use the time to get away from him without engaging in melee. This allowed to get some of his shields down quickly so that he destroyed the first segment of floor while regenerating. This was extremely helpful - if you engage him too long without cover his warp bullets will overwhelm you and force you to use many medkits in a row before your shields recharge.

I don't know about the lower difficulties, but on insanity the troops he summons pose the largest threat: Assault troopers flushed my position with grenades so that the snipers/phantoms could finish me off. Eliminate them first and Leng will be easy picking. For this, I used the Avenger loaded with inferno rounds to down the troops and had EDI keep a decoy up to draw fire and grenades.

It helps to keep your squad separated. By having them hold different positions you thin out the amount of grenades you experience in your hole, and allow for crossfire to pick off the enemies faster. If Leng attempts to melee one of your squadmates, it is a free headshot too.

Through the whole battle I managed to keep Leng from recharging his shields with a BW round to the head every so often. Here adrenaline rush is crucial - a miss wouldn't do, plus the damage bonus helps significantly.

Once his shields are down he is cake: a single headshot with a disruptor round took his head clean off. The battle may not end on his death if any troops are remaining.

I'm an infiltrator, and I had no problems with this fight. I took EDI, and Kaiden. If you have EDI use a decoy, the cerberus troops generally attack that. If not Kaiden, I'd have taken Garrus. I had Liara on her home planet and had a very hard time with that fight. For use, cloak and get away from Kai Leng, then he won't attack you. I love my sniper rifle, and if you do head shots, in about five shots he's done. He doesn't do well against them, and since he is fairly stationary that fight, it makes him an easy target. Also, sniper rifle is effective again Phantoms and Nemesis, you can one shot them which is also handy.

A fully upgraded Geth Shotgun while using Disruptor Rounds seemed to work. I only went into a melee cutscene once in the initial charge. I had Garrus with me, but he was more or less keeping the minions occupied while I felt with Kai Lan. Three charged shots put him down on Insanity. Note this was after his third time breaking the floor though.