Sorry about your hen. She may be dying of a reproductive disorder, but cancer and crop problems can also be common. I would put her down since she looks to be suffering. I use a sharp knife to cut the jugular veins on each side of the neck, but many use the broomstick method of cervical dislocation to put a chicken down.
When one acts like yours, it is good to separate them at first and give them Poultry NutriDrench or electrolytes, and encourage food and water. A watery mash of chicken feed, some cooked egg, and water can be held up to the beak to keep them nourished. When the others start pecking them, that is usually when it is time to put them down. It is never easy, but something we all eventually have to deal with when they become ill.
