This mission will be a bit shorter than the last, but not for a lack of options. Your mission is to kill the two Pendleton brothers, but the ways in which you can complete this objective (or subvert it, if you're looking to get through with clean hands) are quite varied. Before you can enact any sort of vengeance, though, you will have to sneak into the Golden Cat lounge. And before you can even do that, you'll be tasked with hunting down some Weepers in the sewers. Choke them out if you're looking to get Clean Hands - yes, even killing a Weeper is too much for that Achievement. This will make things especially tough in later missions. Anyways, get past the Weepers and grab the two Runes from the far end of the tunnel; one of the Runes will be underwater, so don't neglect to look for it.
Return to Admiral, Martin, and Pendleton once you've completed the task. Stunning a Weeper instead of killing it will get you props from Piero, along with two free Sleep Darts. While you're talking with Piero, buy some items for your next mission. Try to buy upgrades that conform to your playstyle. If you want to sniper or avoid guards, using the mask zoom can be helpful. Range and accuracy for the crossbow would also be must-havs inthat scenario.
When you're ready, get on the boat with Sam.
When you arrive, you will have to go see Slackjaw about the Pendletons. There will be a turret and a watchtower down the street, so steer far clear of the alley off to the side for now. Meeting up with Slackjaw is a necessity if you want to avoid killing the Pendleton brothers. Head into the brewery and speak with him. He will ask you to locate a missing thug named Crowley, and get the safe combination for the Artist's safe. You'll have to visit the Golden Cat one way or another, because the combination to the safe is hidden there. Inside the artist's safe is an invitation to the Boyle Party, an item that will help you out later on.
The distillery may be mildly infested with Weepers if you helped Grann yRags out before. After you finish speaking with Slackjaw, Weepers will attack as you leave, but only if you helped out Granny Rags.