Key Items are a necessity to beat the stages of Prodigy. They cannot be bought, and they have to be obtained directly from quests.
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.
The TEK-Y4 is a dancing robot that you obtain from Lamplight Town to play a certain minigame.
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.
Dyno Dig Shovel
The Vine Pruner is used to trim vines in Skywatch.
The Vinecinerator 2000 is used to trim vines in Skywatch. It is stronger than the Vine Pruner.
The Breathing Bubble is used to go underwater in Shipwreck Shore.
The Sonic Blaster is used in Shipwreck Shore.
The underwater camera is used to take pictures of the mysterious creature in Shipwreck Shore.