I hated getting that weapon... what a pain in the arse... Here are the items you need for the Synthesis shop:
(SPOILER)
Lucid gem x5
Power Gem x5
Thunder Gemx5
Mystery Goox3
Gale x3

You can get mystery goo from the Rare truffles in Monstro but its annoying ... best way to keep them in the air, is to cast Aeroga so they keep bouncing off the shield.. you can get them for about 25 bounces before the shield goes away...

Best way to practice it is to go to the Hercules Cup and do over the Rare truffle over and over until you can do it with your eyes closed and then WHAM you are in Goo heaven! You can;t get goo in the cups, they don't count...

Other locations for the RT:
(SPOILER)Bridge at Halloween Town
Ship's deck at Neverland
6th seed at Hercules Cup
46th seed at Hades cup
Linked Worlds part of Hallow Bastion
Throat of Monstro