Well there must be someways to unlock the academy. You must collect the 5 gems that landed in different places of the map.
Firefly Forest- In Firefly Forest ,complete a quest for Flora ( the forest fairy ) to reclaim her forest from monsters, thieves, and a sleeping giant. While you help Flora you are going to learn earth spells. When you finish the quest you would have the Firefly Gem as a gift from Flora for helping her.
Shiverchill Mountains- On the cold Shiverchill Montains, help Bok light up his furniture to unfrozen the his mountain and help him reclaim his throne from the monsters. Meanwhile you are going to learn ice spells. At the end you are going to receive Shiverchill Gem repercenting that you finsh helping Bok reclaiming his throne.
Skywatch- Vines! Monsters! Cloud Boss! Help Bennie and Broccolina clear vines that covered the rain,wind and snow machine. You would receive more than a gem but also 2 vine burners! They were Vinecinerator 2000 and Vine Pruner ( wand ). At the end you will have the Skywatch Gem.
Bonfire Spire- Now you are working in a volcano to help Slurpylearn how to cook for the queen. Near the end of of the adventure you would have a lava boot to walk across the lava to get back your receip. At the end you would get the BonfireGem.
BarnacleCove- Help Captain Eve to defeat the pirate that stole Eve's tresures. You could learn 4 water spells while helping her and " change your name".Sadly due to the acadmey updating inside, the water gem was took away so no one could go in the academy while up date, so there is no water gem now , to bad. :(