You need both The Looking Glass Tower and the Tome of Magic for this.
Talk to Esmerelda at the Academy of magic first then get Elazul to join you at the Domina Pub. Go into Geo and talk to Esmerelda when she is in the classroom. Talk to her again when she is in the library, then again in the classroom and one more time in the library. She will join you at this time.
Now go to the Palace of Arts and talk to Kristie. Head downstairs and talk to Diana. Once this is done head to the principal's office when it is Dryad Day. Head into the cafe and talk to the Teapo behind the counter. Go back to the Geo map and back into the cafe. Find Elazul at this point and say "a note came". You will then meet up with the inspector at the school and head back to the Palace of Arts. Talk to Kristie and then Diana again.
This will lead you to a battle with the Jewel Beast. It moves slowly, letting you avoid attacks easily. Use quick attacks and techniques to defeat it.