Item Synthesis

Once you obtain the from sealing Agrabah's keyhole, return to the Accessory Shop in Traverse Town. Here you can use the Trinity to access the Item Synthesis Shop.
This shop run by the moogles is a great place to get very rare and valuable items made from the materials enemies have been dropping. At first, the list of items is very small. However the more you synthesize, the more items become available. In order to complete the entire Synthesis list, you will need to synthesize one of each item. The grand prize, so to speak, is Sora's Ultima Weapon. Synthesizing the weapon is the only way to get it.
Below is the entire Synthesis list, broken into the separate lists. To the right of this list is the materials, and what enemies will drop them. Remember that any item can be made multiple times, with the exception of the Ultima Weapon.

Item Ingredients List I Cottage Bright Shard x2 Blaze Shard x3 Elixir Blaze Shard x2 Frost Shard x2 Thunder Shard x2 Mythril Shard x4 Energy Bangle Power Shard x2 Frost Shard x1 Power Chain Spirit Shard x2 Power Shard x2 Guard Earring Spirit Shard x2 Thunder Shard x1 Dark Ring Lucid Shard x2 Bright Shard x1 Mythril Shard x2 List II Mega-Potion Blaze Gem x1 Frost Gem x1 Thunder Gem x1 Mythril Shard x2 AP Up Spirit Shard x3 Spirit Gem x2 Mythril x3 Angel Bangle Spirit Shard x3 Power Shard x3 Bright Gem x3 Magic Armlet Blaze Shard x3 Frost Shard x3 Thunder Shard x3 Mythril x2 Golem Chain Power Shard x3 Power Gem x1 Lucid Gem x1 Master Earring Lucid Shard x3 Lucid Gem x2 Spirit Gem x2 List III Mega-Ether Blaze Gem x3 Frost Gem x3 Thunder Gem x3 Bright Shard x5 Bright Crystal x1 Defense Up Lucid Shard x5 Lucid Gem x3 Lucid Crystal X1 Mystery Goo x1 Gaia Bangle Power Shard x5 Power Gem x3 Bright Crystal x1 Rune Armlet Blaze Gem x2 Frost Gem x2 Thunder Gem x2 Mythril x3 Heartguard Spirit Shard x3 Power Shard x3 Power Crystal x1 Three Stars Blaze Shard x3 Frost Shard x3 Thunder Shard x3 Orichalcum x1 Shiny Crystal x1 List IV Megalixir Bright Shard x5 Bright Gem x3 Bright Crystal x1 Shiny Crystal x1 Gale x2 Power Up Power Shard x5 Power Gem x3 Power Crystal x1 Mystery Goo x1 Orichalcum x2 Titan Chain Spirit Shard x5 Spirit Gem x3 Lucid Crystal x1 Atlas Armlet Shiny Crystal x2 Mystery Goo x1 Orichalcum x3 Gale x1 Crystal Crown Lucid Crystal x3 Power Crystal x3 Shiny Crystal x3 Bright Crystal x3 Ribbon Blaze Gem x5 Frost Gem x5 Thunder Gem x5 Bright Gem x5 Gale x3 Final List Ultima Weapon Lucid Gem x5 Power Gem x5 Thunder Gem x5 Mystery Goo x3 Gale x3

Item Dropped by Mythril Shard Barrel Spider Behemoth Pot Spider Mythril Angel Star Behemoth Blaze Shard Red Nocturne White Mushroom Blaze Gem Bandit Fat Bandit White Mushroom Frost Shard Blue Rhapsody White Mushroom Frost Gem Sea Neon Sheltering Zone White Mushroom Thunder Shard White Mushroom Yellow Opera Thunder Gem Aquatank Screwdriver White Mushroom Lucid Shard Shadow White Mushroom Lucid Gem Gargoyle White Mushroom Wight Knight Lucid Crystal Darkball Spirit Shard Large Body Soldier White Mushroom Spirit Gem Air Soldier White Mushroom Power Shard Bouncywild Powerwild White Mushroom Power Gem Air Pirate Battleship Pirate White Mushroom Power Crystal Wyvern Shiny Crystal Wizard Bright Shard Green Requiem White Mushroom Bright Gem Search Ghost White Mushroom Bright Crystal Defender Gale Angel Star Invisible Mystery Goo Black Fungus Rare Truffle White Mushroom Orichalcum Behemoth Invisible If you truly want to go for all the items in the list, there should be a few things done first. 1-When choosing your weapon in the Dive to the Heart, you want to choose the Shield. This will give you the Lucky Strike ability at level 15, rather than 39 with the staff, and 69 with the sword. 2-Do not battle with Maleficent in Hollow Bastion, until you get 13 Bright Shards, and 23 Power Shards. Once you pass this point, the enemies change in all of the worlds, and these two items become insanely difficult, if not impossible to find. Listed below are the first encounters with about 90% of the items you need to get. with the Lucky Strike at such a early level, you should have little to no problem breezing through the Synthesis list.

Power Shards x23, Bouncywilds	Spirit Gem x7, Air Soldier Frost Shard x9, Blue Rhapsody Spirit Shard x18, Large Body Blaze Shard x11, Red Nocturne Bright Shards x13, Green Requium	Blaze Gem x11, Fat Bandit,Bandit Mythril Shard x8, Pot Spider
Complete 13 Bright Shards Here	Thunder Gem x16, Screwdriver, Aqua Tank Frost Gem x11, Sea Neon	Lucid Gem x11, Gargoyle Bright Gem x11, Search Ghost
Power Gem x12, Air Pirate, Battleship, Pirate	Lucid Crystal x5, Dark Ball Bright Crystal x6, Defender Shiny Crystal x7, Wizard Power Crystal x5, Wyvern	Gale x6, Angel Star

While going after these sets of items, not only will you be able to complete the Synthesis list much faster, but you will gain a major boost in levels from doing so. As stated before, the items should be aquired before you battle maleficent in Hollow Bastion. Once you fight her, and save Kairi, this listing will no longer be valid.
Also remember you will need 6 Mystery Goo, and 6 Orichalcum. The Mystery Goo is dropped by various Mushrooms (See the Mushrooms section for more details.) The Orichalcum can be found by completing the side quests such as: 99 Dalmations, Postcards, and Trinity marks. Complete these three side quests, and those Orichalcums are yours.