In pursuit of 100% completion of this game, I ran into a lot of difficulty with The Imposter Synod. Jade's 100% achievement guide was helpful for others I was missing, but it took me about 5 additional playthroughs to find a working combination of options for this one. Spoilers abound, so please only use this guide if you're OK with that.

I was not able to get the achievement by improving relationship with Theophilus at all. So this guide focuses on Ivy's ritual specialty. In my failed runs, I also tried a couple variations of Milton's involvement, but when I was successful I never even unlocked the Devil's Townhouse location, so that is clearly not a necessary condition. Here's what worked for me:

• Choose the Tailor background, because I think this gives you a solid starting ground with Ivy.
  
• At all opportunities, seek positive interactions with Ivy.
  
• During the first phase of the game, ensure that you complete the Hallowmas ritual with someone. If the pathway is not apparent, ask Horatia if she needs help with anything, and she should prompt you to do it for someone in the household.
  
• After the murder, cultivate positive relationships with David and Phoebe wherever possible.
  
• For investigation, ask Ferret about arsenic sales. Ask Ivy about motivations for Phoebe to get the intel about Phoebe's unrequited love. This will cost you two pennies, so have that on hand.
  
• After his return, speak with David and steer the conversation to his difficult memories. Promise to help if you find a way.
  
• Then speak with Ivy - she may or may not have already told you about removing memories from the grieving mother, but she is the only person who can do this. If your relationship is good enough, you can ask it as a favor. If not, you can pay her four pennies to visit David.
  
• Arrange the mystery solution with "Poisoned candles" up top, "David spurned after an affair" and "Phoebe brought in candles/brought in sigil-marked candles" as your conclusion.
  
• Go to the Laundau's house and choose "Confront Phoebe about murder by arsenical candle." In the resulting dialogue, she will ask about support as she faces hanging. There should be an option of something like "I know someone who specializes in rituals," choose that.
  
• Then go talk to Ivy, asking about support for the accused.

You'll know you've succeeded if the trial goes forward with Phoebe confessing on the stand to David, then the judge saying "you'll have to talk to a priest." It should zoom out and Ivy is there (Screenshot).


This is my first guide, so I welcome any thoughts or clarifying info! I hope it helps someone else, this was a tough thread to untangle.