Here is the full list of all 20 Spellcaster University achievements.
Achieve a reputation with the king of 100.
Have 5 dragons of different colors.
Train at least 10 librarians during the same campaign.
Finish a level with all three objectives completed.
Achieve a prestige of 100.
Have at least 50 students.
Have at least 10 teachers in your school.
Slay an orc.
Pay to draw 10 Shadow cards in the same game.
Achieve a reputation with the orcs of 100.
Train an archimage.
Having 5 different classes.
Have 5 different kitchen utensils.
Use the power of the guidance counsellor to change a student's future.
Discover if the turtle is a male or a female.
Have a reputation of -100 with the inquisition.
To own 5000 gold pieces.
Win a campaign.
Win a campaign in difficult mode.
Start Spellcaster University on the day of the Beltane festival.