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