Key Items are a necessity to beat the many stages quest sets of Prodigy. They cannot be bought (exception of a few notable ones), and they have to be obtained directly from quests or occasionally given by Master Wizards.
List of Key Items
The island map is obtained from Noot at the beginning of the game after completing the tutorial. It allows you to easily travel to different locations on the map.
"A map of the entire island!"
The TEK-Y4 is a dancing robot that you obtain from Lamplight Town to play a certain minigame.
"A dancing robot with a neural network processor for dance move acceleration and increased groove accuracy."
The Vine Pruner is used to trim vines in Skywatch.
"A fiery wand that burns away those pesky vines."
The Vinecinerator 2000 is used to trim vines in Skywatch. It is stronger than the Vine Pruner.
"Having trouble with vines that are too thick to burn with your Vine Pruner? Not to worry, here's your Vinecinerator 2000!"
Boots of Hotwalk
The Boots of Hotwalk are a key item to complete the quests in Bonfire Spire. You can only get them after Cebollini takes your dish from you. They allow you to walk on released lava when Cebollini steals your secret ingredient. There is a chest that holds them, but it requires a key. To get the key, you must defeat several monsters until one drops the key. Then, when you approach the chest, you will awaken a monster that you will have to defeat (a Flame Creator) to open the chest. Inside the chest contains the Boots of Hotwalk.
"These boots will allow the wearer to walk on lava."
The Breathing Bubble is used to go underwater in Shipwreck Shore.
"Allows wizards to breathe underwater."
The Sonic Blaster is used in Shipwreck Shore.
"Used to break up ink blots underwater, this sonic gun was key to helping the pirates defeat the Order of Influence's ancient beast in a war fought long ago."
The underwater camera is used to take pictures of the mysterious creature in Shipwreck Shore.
"Can be used by wizards to take a picture underwater."
Dyno Dig Shovel
"Use this special shovel to play the Dyno Dig game where you can dig up Dyno fossils to fill the museum."
A special key item obtained in the new Academy Update on late September 2018's Academy Quest opening cutscene. This is your source of teleportation power to get you inside the Academy-Great Hall area from the use of the Island Map.
"An amulet given to you by Gale, the Academy's Keeper. It allows you to enter the Academy."