i will try to make some sense of this:

kami = god, hime = princess.

in many folk lore tales, deities are associated with "weapons". obtaining the godly weapon will allow the user to wield the power of that god.

the mirror https://en.wikipedia.org/wiki/Yata_no_Kagami is created by the goddess Amaterasu, so using the mirror will yield the legendary power of purity

the hammer https://en.wikipedia.org/wiki/Mjölnir is used by the god Thor. obtaining Mjollnir will also wield the power of Thor.

the https://en.wikipedia.org/wiki/Trident is used by Poseidon

in this game, when you obtain their legendary weapon for the FIRST time, you will unlock the godess that wields the said weapon in their respective legends.