Hey can you give me a help to understand why this choice of kanji?

皆既食

Eclipse seems to be 日食 or 月食. I guess the image is that the sun or the moon is "eaten" by the eclipse. 皆既食 might mean that it has "already been eaten in whole".

Uhm, nice way to put it.

In the entry for 皆既, Koujien says "（「既」は尽きるの意）".