These are the items that you need to use in order to create new Items.

Item Name – Where to find it
Blaze Gem – Bandit (Agrabah), Fat Bandit (Agrabah), White Mushroom – When last spell casted is Fire (Found Randomly)
Blaze Shard – Red Nocturne (Wonderland), White Mushroom – When last spell casted is Fire (Found Randomly)
Bright Crystal – Defender (Hollow Bastion)
Bright Gem – Search Ghost (Atlantica), White Mushroom – When last spell casted is Cure (Found Randomly)
Bright Shard – Green Requiem (Traverse Town), White Mushroom – When last spell casted is Cure (Found Randomly
Frost Gem – Sea Neon (Atlantica), Sheltering Zone (Atlantica), White Mushroom – When last spell casted is Blizzard (Found Randomly)
Frost Shard – Blue Rhapsody (Traverse Town), White Mushroom – When last spell casted is Blizzard (Found Randomly)
Gale – Angel Star (End of the World), Invisible (End of the World)
Lucid Crystal – Darkball (Hollow Bastion)
Lucid Gem – Gargoyle (Halloween Town), White Mushroom – When last spell casted is Gravity (Found Randomly), Wight Knight (Halloween Town)
Lucid Shard – Shadow (Traverse Town), White Mushroom – When last spell casted is Gravity (Found Randomly)
Mystery Goo – White Mushroom (Found Randomly)
Mythril – Angel Star (End of the World), Behemoth (End of the World)
Mythril Shard – Barrel Spider (Neverland), Behemoth (End of the World), Pot Spider (Agrabah)
Orichalcum – Behemoth (End of the World), Invisible (End of the World)
Power Crystal – Wyvern (Hollow Bastion)
Power Gem – Air Pirate (Neverland), Battleship (Neverland), Pirate (Neverland), White Mushroom – When the last spell casted is Stop (Found Randomly)
Power Shard – Bouncywild (Deep Jungle), Powerwild (Deep Jungle), White Mushroom – When the last spell casted is Stop (Found Randomly)
Shiny Crystal – Wizard (Hollow Bastion)
Spirit Gem – Air Soldier (Agrabah), White Mushroom – When the last spell casted is Aero (Found Randomly)
Spirit Shard – Large Body (Traverse Town), Soldier (Traverse Town), White Mushroom – When the last spell casted is Aero (Found Randomly)
Thunder Gem – Aquatank (Atlantica), Screwdiver (Atlantica), White Mushroom – When the last spell casted is Thunder (Found Randomly)
Thunder Shard – White Mushroom – When the last spell casted is Thunder (Found Randomly), Yellow Opera (Traverse Town)