You cross a crow with a pheasant and you'd have one of the hardest birds to catch let alone shoot!
Crows are one of the more intelligent birds on the planet. Some can make the most well trained parrot look like a backyard sparrow.
Imagine a bird that can run fast, and would have sentries posted to warn of your approach?
(Crows do that to warn of possible attack from hawks, falcons, osprey and eagles.)
On a plus side, they do tend to flock in very large numbers (for said protection) so you find them, you find A LOT OF THEM!
They did a nature show on PBS some years back where they had crows solve intricate puzzles in order to get a piece of food (that they could see) and all the tools they would need were within reach. They were able to get the food after they learned what wouldn't work. It was quite interesting to see them got at it.