Here is the full list of all 26 √Letter - there are Root Letter - there are achievements.
Finish Chapter 2.
Use the "Check" command 200+ times.
Finish Chapter 1.
Use the "Check" command 100+ times.
First conversation with SHIMANEKKO.
Finish Chapter 3.
Finish Chapter 4.
Finish Chapter 5.
Finish Chapter 6.
Finish Chapter 7.
Finish Chapter 8.
Finish The Bond of Marriage Chapter 9.
Finish The Bond of Marriage Chapter 10.
Finish Crossing Paths Chapter 9.
Finish Crossing Paths Chapter 10.
Finish The Princess of Himegamori Forest Chapter 9.
Finish The Princess of Himegamori Forest Chapter 10.
Finish The Cursed Letter Chapter 9.
Finish The Cursed Letter Chapter 10.
Finish A Government Plot Chapter 9.
Finish A Government Plot Chapter 10.
All routes completed.
Acquired all items.
Complete the Cursed Letter Route, Princess of Himegamori Forest Route, A Government Plot Route, and Crossing Paths Route.
Select all letter replies.
Spot SHIMANEKKO 10+ times.