Ziggurat 2

To gain mastery, you need to use a character, or have an item equipped. You don't really need to USE the item in question, its mastery goes up as you clear floors/gain experience. I tested this by taking a new wand and alchemy weapon on a mission. I didn't use the alchemy weapon at all, only my wand, and when the mission finished, I had a mastery level and a half unlocked for both.

To make this easier to do, I would either choose a character you are comfortable with, or choose a beginning amulet. As you unlock more weapons/amulets, the ones you can pick for missions are cycled around. Meaning having only 4, say, wands or amulets means you can keep choosing the same one, where as having everything unlocked leaves it more to RNG.

Getting a mastery level also unlocks an "insight", basically a skill point to use in the lab, so there IS benefit to having different equipment... just not for this cheevo.

Happy hunting (>*_*)>