At the start of this mission, you will find yourself back in the hub town. Purchase everything you want from Piero, because you won't be able to get anything for a while afterwards. Then, head to the bar and drink from the bar. Head up to bed.
You'll wake up in a cell. Escape by possessing a rat or throwing bricks against the wooden paneling to break it. You'll have to face off against two assassins. You can easily sneak past them, or kill them if you please. Leave and look to the top right of the area outside. This is the building from which you'll need to recover your gear. Technically, this is an optional objective, but absolutely do not go without completing it.
The building near the entrance of the map has a Bone Charm hidden atop it. Blink up to it to grab it, then move on. Sneak through the water past the River Krust; they're tough, so you'll want to skirt around them using Blink if at all possible. If you must battle them, use the grenades from the Overseers scattered dead around you.
You'll find a Sokolov Painting hidden in one of the apartments lining the main street. Stand on the bridge and look towards "Daud's Base." The apartment will be ahead and to the left.
Blink to the top of the building to the right and sneak around the pipes on its outside to recover your gear from the room inside. There's a Rune sitting in the open by the swamp along the way. It's covered by River Krusts, so you'll have to kill them to get past. Clear the area to retrieve the Rune safely.
Now that you've gotten the Rune, you'll have to find an empty whale oil tank. Luckily, there are plenty in the lobby. Grab one, take it to the control booth using Blink, and fill it. Pull the lever to activate the stairway. Climb to the top of the building and drop through the broken floorboards to find a Bone Charm. Head back up and you'll encounter some assassins searching for you. Wait for them to leave before heading into the building proper. Head to the upper level and grab the whale oil tank. Fill it in the dispenser and return to the lower level to activate the drawbridge.
Sprint past the Weepers, grab your gear, and head back outside. Follow the waypoint to Daud's base, pickpocketing or looting the Station key from the assassins outside.
The next area will be filled with assassins. Take them out silently from above, or move past them using your powers. At the entrance to Daud's building, head into the alley with the hounds. You'll find a Bone Charm on the lower level, under a dumpster. Now, climb up the chain by the waterfront to get into Daud's base. You'll find a safe underwater, but it's locked. The combination is 428. Now enter the building.
Take out the two assassins in front of the tunnel and take Daud's key from their corpses. Daud will be in the next room. Take out the sentries around him first, either through lethal or non lethal means. Now it's time to take care of Daud. Note that he carries a Bone Charm, and you'll have to pickpocket or loot him to get it. Take ou all of the guards around him first, and then attack him. You'll have to do battle with Daud now. Keep on your toes, and keep your finger on the block button. Counter his melee attacks and then retaliate with one of your own. Don't worry about killing him, as it'll be a choice at the end of the fight. For now, just deal as much damage as you can and keep popping health potions. When the battle is over, you can shoose to either kill or spare Daud. Grab his key and enter the tunnel below to find a Rune.
You'll also find a Bone Charm and a second Rune here. Head to the right to find a Charm on a rowboat, and then Blink up to the roof of the apartment with open windows to find a Rune.
Now enter the sewers. Use the Sewer Master Key to get in; it can be found behind the River Krusts. Don't neglect to get the Bone Charm in the safe along the way. The combination is 528. Swim through the underwater tunnel and you'll come upon Granny Rags and Slackjaw. You can now choose to battle Granny Rags, or simply leave Slackjaw to die. Help Slackjaw if you want Clean Hands; otherwise, you'll have to kill him. Either follow Granny's instructions, or head up to Granny's quarters and grab the cameo on her pillow. Open the furnace and toss the cameo in to kill her.
Grab the Rune from Granny's home and nab the Sokolov Painting from the same room. Jump into the stream and follow the current down to the sewer gate. Unlock the grate with the Master Key and head into the encampment ahead. It'll either be filled with survivors (low chaos) or weepers (high chaos.) Look in the ditch ahead for another Run, and pass the NPCs and search past the River Krusts for a Bone Charm. Leave the area through the door ahead.