Does a Beholder eye ray break its Invisibility?

[ProsecutorGodot]

You are saying here that they require a character to make a save or something detrimental will happen to them. That would be an attack action at my table. In this instance the Beholder would lose invisibility.

And you're free to rule otherwise, but by the rules an attack must involve an attack roll to be considered as such. This is how we've come to accept the strange conclusion that while Magic Missile is an offensive spell being cast that damages the target, it does not count as making an attack against them.

RAW is a strange beast and you're encouraged openly by the developers to use your own judgements where the written rules don't work for your table.