I also had a female leopard Gecko loose her tail due to a rat attack, it took her a week or so before she started to eat again she lived another 6 years her tail did grow back and she lived to the age of 18, best of luck to you and your lizard hope it turns out alright
That's a significant amount of a tail and on top of that cats carry different germs that can be deadly to poultry and other animals so you definitely want to get her to a vet so that she can get some antibiotics she's flipping over probably because it's a balance issue on top of that if she is got an infection it could be swelling in her head and you will lose her so time is of the essence good luck God bless
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