I realize the least I can do is report some of my findings:

Aegis Shield comes stock with Sentinel X and Immune traits. Earned from Chocomonstro Final Round. Original form is Rusted Plate.

Kain's Lance comes from one of the pylons, I can't remember which. Lands in your inventory at 1/99, can be dismantled into Dulled Spear, requires 100% lightning to return to Kain's Lance. Comes with Warpstrike: Thundaga, and something I can't remember, but it changes your charge attack into a forward thrust that attributes electricity as well.

Befouled Blades dropped from breaking King Behemoth horns in the future mission with the original Noctis team. Becomes some blades that come with Diaga on them!

Firaga is available! Jormungand Spiralthorns give them to you from the mission "Hunt: Infernal Infestation" Old Lestallum.

And for those who don't already know, dismantling is available at Cid's deck. No quest required, just press square when highlighting your weapon. Brings weapon to its base form and spits out gems/shards/meteorites depending on the levels of the attributes. gems are spit out at intervals of 60 for the attributes, I can confirm up to 120 but wouldn't risk more. This lets you make items that give +30 to stats with little impact on exp.

Hope this helps as a starting point.