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