This is what I did to unlock this achievement:
1. I gave peace to Sophia (might not be necessary)
2. I finished the game with the "Rise of P" ending (achieved by lying and refusing to give your heart)
3. Do NOT start New Game + right away, rather press
when prompted after killing
4. Go to Geppetto's desk at hotel Krat and find a blue letter called "The Blue Butterfly's Letter"
5. Find the letter in the collectables tab and press
to read it and the achievement should pop
Add any suggestions or steps I might've missed in the comment!
EDIT:
Apparently you need a lot of humanity (to lie throughout the playthrough) for this to work. A good indicator is that your hair should first become long and then gray near the end of the game. If you told truth throughout the majority of your playthrough the letter and the correct ending might void.