Prerequisites
1. Completed both Granny Rag's side quests in Mission 02: High Overseer Campbell. This involves the first one where you deal with the thugs knocking on Granny's door, and the second one where you have to poison the distillery.
2. Complete both of Slackjaw's quests in Mission 03: House of Pleasure. This means the first quest where you need to retrieve information from one of Slackjaw's men in Galvani's house, and the second mission where you need to get the Art Dealer's combination for Slackjaw.
**NOTE** I saw some people say that if you kill the Pendleton's instead of letting Slackjaw deal with them, the event that procs this achievement will be unavailable. HOWEVER, through my personal experience where I had both robbed the Art Dealer's safe AND murdered the living shit out of the Pendleton's, I was able to activate the event in The Flooded District. I even got the dialogue when turning in the Art Dealer's combination where Slackjaw specifically says he doesn't have to hold up his end of the bargain anymore.
Getting the Achievement
The specific event that you need to witness occurs during Mission 07: The Flooded District. Before you get to the camp of either survivors (low chaos) or weepers (high chaos) down in the sewers, you will need to pass through a gate. If you have done the two prerequisites listed above, that gate will be locked. You will then get a new quest marker that leads you to a confration between Slackjaw and Granny Rags.
1. Talk to Granny Rags
2. She will tell you to incapacitate Slackjaw, so just shoot him with a sleep dart.
3. Talk to Granny Rags again and she will give you a key.
4. Use the key on the mechanism beside Slackjaw to free him from the chains
5. Pick up Slackjaw and then carry him over tot he boiling pot.
6. Dump Slackjaw directly into the pot.
7. Talk to Granny
8. Go to the rune that is now labeled as a quest objective. That is Granny's gift for helping her.
9. Cheevo popped
**NOTE** I suggest you make a save before you interact with Granny Rags or else you will not be able to get the Street Conspiracy achievement in the same playthrough.