Here is the full list of all 10 Lachesis or Atropos achievements.
You've achieved Dead End 2
You've gotten Shiki End 2
You've gotten Towa End 1
You've gotten Shiki End 1
You've achieved Dead End 4
You've gotten Towa End 2
You've achieved Dead End 3
You've achieved Dead End 1.
You've achieved Dead End 6
You've achieved Dead End 5