I think that in general I'd rule that because of the mental ability score shift, things like "understanding how polymorph works" is beyond the ken of most normal mice and rats (and most beasts). Your enemy can't turn the effect into a one-round debuff by being clever - they're no more clever than your average rat.
That's fair.
I allow my players to use a reasonable degree of tactics while polymorphed, so for that reason I'd at least give the BBEG an Int/Wis check to do the same.
Polymorph is strange to me because it states that you take on the mind of your animal form, but you retain your alignment and personality. How can a rat be lawful if it can't conceive of what is legal or honorable? If a paladin marks his church while polymorphed into a dog, does he need to atone for doing so? Or would the fact that he retains his alignment and personality preclude him from doing so in the first place?
If one of the BBEG's personality traits is "I will survive no matter what the cost", how does that interact with the fact that he might no longer be intelligent enough to realize that hurting himself is exactly what he needs to do in order to survive?
The way I've handled it up til now is that I tend to give a lot of leeway, based on the fact that while it can be difficult for animals to learn certain things, once they do learn it they can demonstrate surprising capabilities. If the target of the polymorph was formerly intelligent, they've already accomplished the learning part, so IMO they'd be at least capable of functioning at the level of an exceptionally smart animal. If you could teach a rat that biting itself on the paw will chase away predators, I suspect it would do it. Therefore, I'd at least give the BBEG a chance.
Of course, the players could simply get around the issue by polymorphing the BBEG into a frog like I originally suggested. Can't drown it, but it can't bite itself either.
