When I played my last playthrough I went for the Clean Hands achievement and couldn't get it because I had to get past Granny Rags and Slackjaw at their last meeting.

Well if nobody has told you yet (and I hope they have) the secret is NOT TO VISIT GRANNY where she gives you the Gentleman Callers mission.

Why?

Well, if you don't (you can visit Slackjaw later btw) it leads to no final meeting between Granny and Slackjaw and gives you a free pass through the Sewer Grate... no having to grab it off Granny and do the crazy running and blinking and freezing time thing. I tried that and even though I didn't kill Granny I never unlocked clean hands for some reason. Doing it this other way it unlocked Clean Hands and Ghost perfect.

Just have to do the Mostly Flesh and Steel runthrough and I will have maxed out (until the DLC comes out). I do love this game.

Or just freeze time, steal the sewer key from her, and then run away. It's pretty simple and not "crazy" at all. And not only will this let you get Clean Hands, it won't mess up Ghost either as long as you get out of there fast enough, plus you don't miss out on all those runes.

or just take the key from her and run. i didn't even see the "swarm of rats" thats how fast i got out lol.

It's just easier is all. If you are doing a ghost runthrough you get enough runes anyway. It's different if you are doing a combat run though.

I went for the route of freezing time, pickpocketing the key and legging it. Still didn't Ghost nor Clean Hands after beating the game even though I had 0 detections and 0 kills according to all mission screens. (Did get Shadow)

I got Clean Hands and Ghost on the level with Granny Rags and Slackjaw. Wasn't that bad really.

Before approaching either of them, go into her little shack and look around. Read the books, open the furnace, grab the amulet (I always use Dark Vision so it's easy to spot without being told to look for it). Then go talk to Granny and agree to help her. Then, talk to Slackjaw and say you'll "consider it". When Granny's back is turned, choke her out and jump on the rock next to slack jaw to avoid the rat swarm. You can stay there long enough to hear Slackjaw tell you to grab the amulet if you like. Then Freeze Time, and run/blink back up to her shack, toss the amulet into the furnace and close the door. Run around the corner from the furnace in case Granny appears there so she doesn't see you. Wait for the explosion to know the Amulet has been destroyed, then Freeze Time again, and go choke out Granny one last time. Carry her body to her bed, and tuck her in for a nice long nap.

Finally, finish up by talking to Slackjaw (any rats will probably have disappeared by then) to get your reward.

Nobody killed, never spotted, get more gold, and a Rune.

I thought they said choking her out or sleep darting her after destroying the cameo would negate the Clean Hands achievement. I just got there myself and failed, multiple times, to get Slackjaw out without either Granny or him dieing, so I'm just going to steal the key and hope for the best.

For Slackjaw to live, don't set him free of the shackles until after Granny is taken care of. She won't bother him so long as he's still locked up and you agreed to help her. The hardest part when doing it the way I described is not being seen by Granny since she can sometimes teleport right behind you, which is why I said to hide around the corner of the furnace.

The thing here is that you've already got the cameo and the furnace open, and she won't be considered a hostile enemy until after you choke her out the first time (and then she vanishes), so you don't have to worry about Granny reappearing while you're waiting for the furnace. As soon as it's destroyed she'll reappear though. Freezing time and choking her out seems the safest bet here. No rats to bite her and she won't fall and get killed.

It ends up using more spiritual energy than I'd typically like but there are two of Piero's Elixirs right there to give back what you just used.
At the end mission overview thing it had Clean Hands and Ghost both checked off for me. Just make sure Granny is in fact labeled (unconscious) at the end when you plop her down on her bed.

This works for it to show a checkbox next to Ghost on the mission screen and to get it to show as no hostiles killed on the same mission screen, it does however mean you won't get the achievement for Clean Hands when beating the game. Unless this is so buggy that it works for certain people and not for others ofcourse.