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