Help FFXIII: Weapon Catalyst

Yes. Adamantoise (the ones with tusks) and their upgraded versions after completing the circle of missions.

Another way is to obtain 1, 2 mil or defeat said enemies, and upgrade one of Vanilles weapons. I forget which one I think it was nirvana? Get it to level 99 and dissemble it. It will give you three of the items your looking for. It costs a lot of money but I found it easier than the other options.

PS : If anyone wants to help me out here and give the name of the weapon(s) I'm talking about much appreciated! Also the name of the monsters. I know some people will be able to name them right off. I didn't really like Final Fantasy XIII so I don't remember. :(

EDIT : oh and I forgot to mention that if you sacrifice 1 of your 3 genji gloves they turn into the weapon catalyst you mentioned. I think you need the Genji Glove at star level 1st though.
 
Killing Adamantoises are the most efficient way to get the trapezohedron.
You will find that you will have to kill this guy hundreds of times if you feel like achieving all of the trophies in the game.
 
I found that if you get strong enough to beat a long gui and you equip a connoisseur catalog you will get a trapezohedron every time (you will need a 5 star battle rating) alternatively you can upgrade Vanilles Belladonna wand to its maximum, you will need one trapezohedron for this, once you've upgraded to nirvana get it to maximum then dismantle you will receive 3 trapezohedrons plus some other assorted items. Hope this helps
 
You can also get 3 traphezedrons and other goodies by upgrading Fang's Bladed lance to level * and then dismantling it. I think you can get it by replaying the last of Tutan's mission or the behemoth battle in titan's trails or I'm sure it may be available at a shop.

The best way to upgrade weapons though, is to hope over to creature comforts and buy loads of diabolic tails,transparent ooze etc then you could get a multiplier value of 3!
 
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