High Overseer Campbell is your first target. As your first real mission, this one will take much, much longer than the last one, especially as you get used to the game's mechanics in the context of this much larger world.

After you complete the requisite objectives and speak with everyone in the tavern, take the time to explore before going to bed. There isn't a ton here, but you would be well-served to get acquainted with the layout and characters in this area. When you're ready to get your magic on, go to bed. You will dream of the Outsider and earn your first ability, Blink. This teleportation move lets you jump between two points in space instantaneously.

Once you have the Blink ability, grab two Runes before heading out. Use the Heart you received from the Overseer to find the Runes; they aren't too difficult to find here. The first Rune here will be by the water by the fighting pit building. Use Blink to skip over the water so you don't get bitten by fish, and grab the Rune. The next Rune is in Piero's store, so just drop 500 coins for it and equip it. Now you should have three Runes, so head into the menus and spend your Runes before the next mission. While you're n Piero's store, take your time to stick the whale oil battery upstairs into the machine downstairs so that you can buy more stuff from Piero.

Speak with the Admiral when you are ready to proceed, and then head over and talk to Sam.

When Sam's boat docks, get off and look around a bit. There are NPCs here that are peaceful towards you, while the City Watch guards will instantly attack you. If you're not interested in getting the Ghost Achievement, you can carve your way to the Runes and Bone Charms easily enough. Clean Hands isn't too tough to get in this level, either, if you're up to it. There are also many optional tasks to complete here, the first of which is helping out Granny Rags. You should definitely look to help out as many people as you can.

Head over to Granny's house, avoiding the Wall of Light on the main street to head off to the side. Speak with Granny in the corner. She will think you're her husband. This will initiate a side mission in which you must protect her home from a roving gang outside. You'll get a Rune in return for this. In order to kill these guys, head upstairs and jump off of the balcony. Use your drop kill move to take out one enemy for free, and then butcher the rest. They shouldn't be too tough to kill. The only exception here is if you're trying to play through with no kills. You'll have to use choke holds by sneaking around behind the thugs with a Blink. The last two enemies will always spot you no matter what, though, so you'll have to weigh whether or not this mission is worth it in the grand scheme of things if you're trying to play through with no kills. Doing this is possible, but not even close to easy.

Speak to Granny afterwards to collect your reward.