Here is the full list of all 14 Headmaster trophies - there are 11 bronze, 2 silver and 1 gold.
3 Stars on Every Lesson
Ace Every Exam
Bowl 3 Strikes In A Row
Earn your Freedom
Pass Exam 4
Hit Robert in the Head with a Knife Ball
Pass Exam 3
Hit the loudspeaker with a Ball
Pass Exam 2
Catch Robert in the Porta-Potty
Pass Exam 1
Hit large goal crossbar 3 times in a row
Receive the Snack Cart
Perform The Proper Heading Motion