Reverend Uncle Bastard
Both cards say: you may destroy it by inflicting 8 Bullet of 5 Bomb damage on it.
Do you have to use an action to do that? I'd assume so, but all the other cards that require an action, say they require an action.
Pretty sure the answer is yes since the only way to inflict damage is to do an attack, which is an action (unless you find a tactical response card that would somehow inflict that damage). The other cards mention that they require an action for clarity since they differ from regular play, whereas this one requires damage, which requires an attack which is always an action.