Dodge is revealed in the Avoid Attack step. Dodge counts as a defense and defenses are used in the avoid attack step. Saying it must be revealed when this creature is attacked sets up the "trigger" to reveal it. A creature is attacked once it's attacker pays all of the cost associated with that attack and the Attack is "locked in".
So, to be clear Dodge counts as a defense. This means that you can only use it in the Avoid Attack step, and because of its trigger, if you've been attacked then you must reveal it. Also, because it counts as a defense if for some reason your Dodge fails you cannot attempt another defense as you are limited to one defense per attack.
I hope this helps clear things up for everyone.
Sorry... but it seems to me that you are saying two different things:
1) Dodge is revealed in the Avoid Attack step, and
2) It must be revealed when this creature is attacked (which you also define as when its attacker pays all of the costs associated with the attack and the Attack is "locked in") -- which I can see as happening in the Declare step.
Also, does it really matter where the defense is actually used (in terms of when the enchantment is revealed)? You never have to reveal non-mandatory enchantments when they are actually used, after all.
"If a mandatory or single use enchantment is revealed at any time other than the event for which it is supposed to trigger, it has no effect and is immediately destroyed and discarded. You cannot hold the revealed spell, to use its effect at a later time."
I do not believe that this has anything to do with what I was saying. I am not concerned with the revelation of the Dodge, which I believe must be during the (and right at the end of) the Declare Attack step.
My point was that the prior remarks seemed contradictory... that it would be revealed at two different times.
To play Devil's Advocate a little more here though, if I may, I still do not understand why you can't reveal the Falcon Precision after the Declare Attack step. (Or can you, but not have it be effective during the Avoid Attack step for some reason?)
Thanks to all for trying to help me understand.