It would be nice if you also report your findings here. It's not redundant, I assure you. A detailed report make for easy searchs.

I believe you get the recipe for Eushully weapons by completing the base weapon quests (Pinkwing Vacuum/Iron weapons). Maybe you need Ultimate Recipe and/or some Divine Bones too. Sorry I don't have a specific answer.

If you're still curious about the buckets, there are 10 different ones.

This is a list of them with the requirements to get the recipes.
Iron Bucket: Quest Iron Bucket
Maid Bucket: Quest Iron Bucket clear
Eushully Bucket: Quest Iron Bucket clear
Balt Bucket: Quest Balt Bucket
Sand Bucket: Dungeon Burning Sands clear
Ice Bucket: Dungeon Parallel Rivers clear
Charcoal Bucket: Dungeon Thunder Peak clear
Stun Gun Bucket: Dungeon Land Of Regrets clear
Infini Bucket: Meister, Synthesis Rank M, Ultimate Recipe

also:
Dark Gate Bucket: Mutated from Charcoal Bucket

Thanks for the info Ross.

What I figured is that besides the quests, in order to open the new recipes you have to have the previous weapon level maxed, then you will get the recipe if you have already trigged the quest, however I think the quest is just for each class item, up to the first chain.

By the way now I am stuck on fairy wing, it said that fakes phinilly drops it but I already did her event and got her in the party is there another way to get a fairy wing that does not involve lvl 90 dungeons ? I am still weak for those ;( need to think of a good tatic to stand a change.

You're out of luck.
The only place to get the Fairy Wing (Other class item #185) is Phinilly.
That means your next playthrough.
This is an ingredient for Kilonos Retal and Maid Fan.

You may be confusing it with Fairy Wings (Accessory class item #104).
This is Phinilly's unique artifact.
It's a drop from Razorwing which are in Phema Mountains - Thunder Peak. (lv 90)

If you don't have any then that must be the case unless you already used what you did get.
The fakes drop them so if you do it right you can get enough.