You can find the mastery cards through the "Mastery" page in the options menu.
The easiest Mastery Card I found to do was any of the weapon tree Mastery Cards. (You only need to do ONE of the weapons)
I personally used the Shrike Sword. (As the Shrike is quite an easy monster, I didn't need to worry about having to kill a really hard boss repeatedly for a chance at the level 10 crafting materials)
As you only need to craft it, reach level 6 and level 10 crafting level with it, and get a set amount of xp through hunting creatures with it.
The level 6 crafting you will unlock as you progress though the story, when you unlock "Dire" hunts, which are upgraded versions of the standard creatures, which have new loot for part destruction and kills. (so Pangar's upgraded form is "Frost Pangar"
The level 10 upgrade takes it further, with "Heroic" monsters added for the late game, thus unlocking another level of crafting resources from the monsters (IE, Would be "Heroic Frost Pangar)
The xp can be earn in Hunts, with Xp being granted for kills, knockdowns and part destruction
You may need to go in to a new hunt to get this too pop after, as it didn't pop immediately for myself.