I have this same problem with my own cats. I usually heavily sedate them to do the work, because is is work! One needs 30 to 45 minutes of cutting fur, combing and grooming to get a bad one done, and that is just too much for a cat to withstand awake and at 12 years.
Sedation is safe and the least traumatic way to get it done. But Your veterinarian will need to do this for you. Just call them and explain the situation and I'll bet you can get it done reasonably. (FYI: they may want to do some blood work prior because of her age).
Then once done, you can keep up the fur maintenance on your own and never have to do this again.
I agree fully with the above comments. As a holistic veterinarian I have also been faced with many cats like yours and grooming a cat that is matted can be tough. Your vet is always your best 1st choice. Here are a couple natural and very safe remedies you might consider. Melatonin is a natural amino acid that has a calming effect and is very safe. It is available over the counter at most drug and health food stores. I have used this personally and professionally for many cats. A dose of 1.0 milligram given by mouth is effective for most cats to safely calm them so you can get her cleaned up. Bach's 5 Flower Remedy, is a natural mixture of five flowers that is also very safe and also has a calming effect. Bach's is a liquid and 2 drops placed in her mouth, her food or water would be an appropriate dose. I would try the melatonin first. These are both natural, safe remedies and remember it is always best to check with your vet before giving anything to your cat. A professional groomer is another valid option.
Thank you
Dr Carol Osborne, DVM