Pentiment

In act 1, starting day 2, focus your investigation on Sister Matilda.

First go into the church at bedtime and sneak into the crypt, going to the far right. Interact with the baby holding the key to reveal a secret staircase to the library. Going to the 3rd floor you can read the entries of each sister and the mother revealing a dark secret.

(If you stay hidden when two people enter the library as you exit you can also have the chance to seduce Sister Zdena in the morning unlocking the achievement Kiss Zdena)

The next day, through the course of talking to Mother Cecilia, Sister Matilda herself (after talking to Mother Cecilia), Father Thomas, and Brother Wojslav you find she has a very big reason to be accused.

At the end of Act 1 you are questioned by Archdeacon Jacob about your findings and in order to get this Achievement, you need to accuse Sister Matilda (and nobody else) and list your findings as cause.

Once the line of questioning end, you are the Town square to see the execution. Once you talk to Peter and he tells you Sister Matilda is being executed, the achievement pops.

If you don't like this outcome, after the achievement pops, you can pause and quit to main menu and you'll be placed right before meeting the Archdeacon.

Happy hunting!