shore, brink, verge
瀕 centers on the edge of something, especially a body of water: a shore, brink, or verge. The idea extends naturally to being on the verge of a state or event.
瀕 combines 氵 (water) with 頻, which likely contributes the sound and the idea of approaching or being close to the edge. The exact historical development of the component relationship is uncertain.
Water 氵 meets the edge of the land, and the right side 頻 suggests something repeated or pressing close. Picture waves lapping repeatedly at the shore, right on the brink.
For ヒン, imagine standing on the brink of a hinoki (檜, Japanese cypress) forest by the shore: hinoki -> ヒン, and the trees mark the verge.