Dishonored Walkthrough Part 7: The Royal Physician Part 1
You can begin this next mission pretty much as soon as you get back to the hub town. You will want to visit with Piero in his warehouse before heading out on your next quest, of course, and upgrade all of your inventory and save your game. Next, speak to Lord Pendleton and inform him that the job is done, one way or another. You will then have to meet the rest in the Hound's Pit tavern for a very brief interlude before heading back out into the fray. Your new goal is to kidnap Anton Sokolov and use him to find out the identity of the Lord Regent's mistress. By getting to the mistress, you will be able to kill Hiram Burrows and remove him and his government from power, thus implanting the rebels with Emily at their head in the seat of power.
Head over to Sam's boat to get this mission up and running. Sam will ask you to take out the lights on the river leading up to Sokolov's residence. Otherwise, he will be detected in his approach. Leave the boat and head up the south end of the Kaldwin Bridge. You'll see plenty of City Watch on the bridge, so you will need to be especially careful with your approach. You'll come across four guards on the first area in the street. Avoid them if at all possible; even if you're going for high chaos, fighting off all of the guards in this area can be kind of tough. As you move through the streets, check the work station next to the mine cart t o find the blueprint for Galvani Resin.
While you're up here, use the whale oil fuel cell nearby to power up the mine cart. Get in, flip the switch and then crouch in the cart. The cart will take you all the way over the soldiers below, and as long as you remain crouched they won't see you. Now you can either remain content with avoiding the guards, or attempt something flashy like slowing time and taking out every guard below with your crossbow and pistol. Either way you want to go, the mine cart is the best bet.
Sneak out of the mine cart, being especially careful if you decided not to viciously murder every guard below you. There are Runes to be collected here, along with Bone Charms, and you won't want to miss them. The Rune can be found on your way towards the bridge. You'll see a side path leading to a metal walkway pointing towards a dangling chain. Climb up the chain and jump out at the top. Smash through the obstruction in the doorway, and then head in to get a Rune.
A second side exit by the south side gate by the drawbridge entrance will lead you down to a canal filled with weepers. Wipe out the weepers however you can and grab the Bone Charm by the top of the raised lock.