Here is the full list of all 20 Spellcaster University achievements.
Finish a level with all three objectives completed.
Achieve a prestige of 100.
Have at least 50 students.
To own 5000 gold pieces.
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 king of 100.
Have 5 dragons of different colors.
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.
Train at least 10 librarians during the same campaign.
Win a campaign.
Win a campaign in difficult mode.
Start Spellcaster University on the day of the Beltane festival.