Here is the full list of all 21 My Universe - there are School Teacher achievements.
Complete your first class
Complete your first week of class
Complete your first year of class
Pick and hold a dinosaur
Unlock your first item
Reach at least 25 stars in one class
Get your first star
Unlock 10 items
Create your first teacher
Fill the three teacher slots
Gather a total of 100 stars
Gather a total of 250 stars
Gather a total of 1000 stars
Win a contest
Win all Gold contests
Reach the maximum number of students
Explore the school
Complete your first quest
Choose your school name and logo
Meet Willy the Janitor
Clean the classroom for the first time