Here is the full list of all 10 Project Kat - Paper Lily Prologue achievements. It takes around 1-2 hours to unlock all of the achievements on Windows.
Read the full ritual rules.
Found the letter in the theater club room.
Picked a lock.
Recruit the 3 girls into your party.
Reached the wrong ending.
What else is this used for?
You've done the opposite of what I expected.
Reached the true ending.
Completed the ritual successfully.
You should be more careful about the decisions you make.