Blood and feathers can obscure a lot but it does look like half of her face has been ripped off. It is not an envious position to have to be the one to end a pet's life, but it is our duty as owners to do so when the situation calls for it. I prefer a shotgun in situations like these so there is absolutely no doubt in my mind that it is instant. If you have nothing else, get your sharpest knife/chopper, comfort her, say goodbye, grab that neck and behead her as quick as possible. Do not be squeamish as it will only prolong the pain.