Once you've had your conversation with Hugh Darrow you'll have to make your way to the giant elevator to the final boss battle. This one was pretty simple, even for non-lethal and give me Deus Ex difficult.
On your way down make sure you read the pocket secretary that Hugh gave you (if you won the speech challenge). If you want all 4 endings make sure you talk to Sarrif and Taggart, also try to pickup a couple of gas grenades and EMP grenades as they'll make your life easier.
I recommend you have at least 1 gas grenade, and at least 1 EMP grenade. I also recommend a long range weapon that can deal some decent damage (I used a Laser Rifle), as well as some hypo-stims and or pain killers (none of this is necessary but will help).
Your augmentations shouldn't matter but having dermal armor, protection from electricity will help as well as faster sprint and neruo-toxen protection. Again none of this is necessary but it will help.
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After you watch the cut scene the game will have you standing behind a pillar, Run straight to the core at the center of the room as fast as you can. There are ceiling turrets that will shoot at you so the quicker you can get under them the better.
Once you reach the center run along the edge counter-clock wise until you come to a hackable terminal (about 1/4 of the way around). If you won the speech achievement against Hugh Darrow you'll have the code, if not just enter "2012". and set it to deactivate.
Once you've done that continue running along the core counter-clock wise (another 1/4 of the way around) you'll see a room has opened up to your right. Inside are 3 "crazys" that you'll need to take care of. The fastest and quickest way is to simply toss a gas grenade into the room. If you're immune to neruo-toxen then just run in after it, otherwise wait for the smoke to clear before entering. Failing that if you have the double-take down augmentation and a non-lethal weapon (preferably the stun gun) you can use that combination to take them down.
Once you enter the room pick up whatever ammo and health you might need then use the wall to the left of the door for cover. You'll see some robots driving around outside, use your EMP Grenade to take them out.
At this point if you have the laser you can shoot though the glass in front of Zhao Yun Ru to kill her and end the fight. If you don't have the laser you'll have roughly 2 minutes from the time you entered the code until the glass in front of her breaks, once it does shoot her with your weapon of choice. (thanks Anatana!)
I've attached a video (not mine) the method is similar to mine except he used lethal tactics against the crazies which would void the Pacifist achievement.