Dishonored

There is another way to do this, that I found much more badass (:p) than the above solution, although that one is fine too. If you try to approach Daud with time frozen, he'll say "Nice try, Corvo." and begin moving anyway. You get into an epic duel with him and his assassins in which he freezes time as well, and at the end, he gives you a speech and the option to kill him or spare his life. I spared him, and got the achievement!

Edit: The achievement itself unlocks, if you follow this strategy, as you are walking away from him after he's defeated. Not once you leave the map.

Mission: 7 - The flooded District
missable Achievement: yes

at some Point in the your 7th Mission you need to steal a Key from Daud, you get the Mercy is the Mark Achievement for stealing Bonecharm he is waring and the Key from him undetected. You may need to wait a few minutes for the right time to blink in steal the things. If you have Bend Time, its fine too ofc. Don't try to shoot him with Sleepdarts, he is immune to them.

When you leave the Map, you will be awarded with the Achievement.

Here are 2 ways to get this achievement depending on whether you are going for high chaos or low chaos.

If you are going for high chaos: you can either stealth it or go loud. The stealth way will be mentioned in the low chaos one. If you are going loud just fight him. He will call some of his assassin goons. Kill them and don't do any damage on him. After you kill his goons he will try to surrender to you. If he doesn't damage him a little and he will. Choose the option to spare his life.

If you are going for low chaos (I'll assume you are also going for the achievements that you can't be detected, kill anyone, or use anything besides blink) here is an easy way: He is immune to sleep darts so don't even try. Since you can't use any powers you can't freeze time either (although he will be immune to that as well). Many other people seem to say sneak in grab the key and run but it's risky. Now luckily I just tried this and it works, JUST KNOCK HIM OUT WITH YOUR CHOKE ATTACK. Yes it's that simple. Take out the only guard in the room, than blink behind Daud and choke the crap outta him. Grab his key and make your way to the tunnels (careful there will be 3 guards).
The achievement should pop once you reach the tunnels and go into the next area.

So to sum it up:
High profile: spare his life after the fight.
Low profile: blink behind him and knock him out with choke attack. No need to risk grabbing the key only for him to turn around and catch you (always happened to me)

Best way to do this if you want a non lethal playthrough is to possess the guard that stands next to him, walk the guard away through the door behind him then knock him out. then when daud is reading his book next to his desk sneak up behind him and steal his key, DO NOT use bend time as he will catch you by using that power.

p.s you can still get a non lethal on this level even if you have to encounter granny. just stop time, steal the key from her and jump up the stairs get the last painting and rune before you go too!