Here is the full list of all 6 Pocket Academy ZERO trophies - there are 1 bronze, 3 silver and 2 gold.
Proof of employing Kairobot.
Proof of running a school for many years.
Proof that maximizes the level of the 5 challenges.
Proof of becoming a prestigious school.
Proof that there are 6 pop spots.
Proof of carried out a Sp. class.