I think this has been asked before, but can a monster attack while it is sharing the same space as another monster, provided it has the movement to get to an acceptable ending spot when it's done? Can a flying monster attack while over rubble or water?

To the best of my knowledge they can not because both monsters and heroes technically stop their movement to attack.

Movement rules, page 9:

"Figures may pass through spaces occupied by friendly figures during movement, but they cannot attack while in the same space as another figure and they must end their movement in an empty space."

I can't find any rule that would prevent a flying figure from attacking while over an obstacle that blocks movement, though.

Big Remy said:

What's this based on?

Antistone said:

Probably my own addled way of thinking lately. Its more the whole "I move 2 spaces, attack, move 2 more spaces" way of doing Advances.