To start this achievement, go to the Nam Cobanda Island gym (located in the upper left hand corner of your world map) after the final dungeon appears and talk to a Kow on the lower middle of the gym in front of a bunch of books to see a scene with Rita.
Now you gotta go collect some books, located at:
1) Halure's Mayor's House
2) Fortune Market HQ at Torim Harbor
3) Knight's HQ in Heliord
4) Mantaic's Inn
5) Flynn's House in Aurnion.
Return to the Kow at Nam Cobanda Island with the books collected to start a quiz.
The answers to the quiz are:
1) September 30, 1998
2) Raine Sage
4) Presea Combatir
5) Ishtar turns to stone.
You'll unlock the achievement and title for Rita after you answer all the questions correctly.