If Maiden with Eyes of Blue is targeted for an attack and is face down, can it still activate?
Unfortunately, you can't activate a monster's effect unless they are face up.

It is true that at some point you will have to flip Maiden to perform battle calculation, but her effect activates only when she is targeted for an attack as the card text reads.

To use the summoning effect the Maiden has to be face up when targeted for an attack.