Where can I find materials for augmenting Master Rank gear?

All the materials needed for augmenting gear are found in the Guiding Lands. When hunting there, monsters will drop shiny pickups as they take damage; those shinies are the materials you need.

The materials might be Spiritvein bones, stronger versions of regular monster materials, or Spiritvein Gems that are only dropped by tempered monsters. Monster-specific materials can also be carved and received as rewards at the end of an expedition.

Generally, each monster drops a material unique to them, like a scale or a fang, and a different material when fought as a tempered version. Naturally, higher tiers of augments and upgrades require materials from more powerful monsters. You can check what kind of material each monster can drop in the Hunter's Notes, under the Guiding Lands section.

In addition to these dropped items, don't forget to mine and gather bones in each of the regions. These items are also used in upgrading and augmenting, and the more you gather, the better items you'll find.