Martha Is Dead

Starting in chapter 8, you can use the telephone to call various numbers in town to have conversations to advance the story and get additional background information. Most of the numbers will also appear on the notepad by the telephone. Below are the numbers, along with the chapter I was in when I used them and the conversation options I used for each - you select the option by pushing the left stick in the direction indicated on screen. Note - the notepad also lists a number for "Shop" as 6539 - I tried calling this number and it never worked, it appears to not be required for the achievement.

Chapter 8: The Burial
6978 - Carabinieri (police headquarters)
Request Information
Act as Mother
Say Goodbye

6987 - Haberdashery
Act as Mother's Friend
Request Information
Insist

6934 - Lapo's Contact (number is not on the notepad, it is located on your objectives after reading the letter you found at the end of chapter 7 - this call may not be required for this achievement, but it is needed in order to start the side-quest related to the achievement "The Lovers")


Chapter 11: The Graveyard
6593 - Doctor
Act as Yourself
Yes
Good

1185 - German Command (only works after speaking to the doctor in the previous phone call - this number isn't on the notepad, it can be found on the letter on the desk in the study by radio, which is available to view from the fist time you can enter that room)
Act as Mother
Side Effects

6537 - Cemetery
Act as Yourself
Be Calm

6938 - Don Attilio (priest)
Lapo

Do these after you read the telegram that was delivered when you go downstairs
0782 - Asylum
Request Information
Lie

6922 - Town Hall
Ask about Admission
Request Information
Say Goodbye


Chapter 12: Memories
6938 - Don Attilio (priest) - do this after the second puppet theatre sequence, you only have one option for each response