Here is the full list of all 30 Valthirian Arc: Hero School Story achievements.
Ascend Isabel to Mother Seat.
Support one Queendom to rule the Realm.
Graduate 50 students.
Unite all Five Queendoms.
Obtain Shermanstaff.
Learn an ultimate skill.
All facilities built at Accreditation level A.
Reach Accreditation level A.
Rename a student.
Obtain Valthir.
Obtain Crescent Edge.
Finish Chapter 4.
Promote a student to Harlequin.
Promote a student to Scholarsage.
Promote a student to Paladin.
Enroll 30 new students.
Finish Chapter 3.
Craft 10 accessories.
Promote a student to Arquebusier.
Craft 10 weapons.
Have 1,000,000 G in your Academy's funds.
Promote a student to Arc Draconus.
Promote a student to Medica.
Finish Chapter 2.
Finish 30 errand missions.
Finish Chapter 1.
Buy an item from the wandering merchant.
No fallen students for 5 consecutive missions.
Graduate a student.
Unlock all achievements.