You may very well have to have her shaved. My mom does this with her Persian. She gets a "lion" cut, or you can simply cut the bad tangles out. I will give you several tips that I have found work for my cat:
Take a baby-wipe and spray it with lots of hair detangler made for kids. Then while your cat is eating a food she loves (like wet food) or someone is holding her, wipe this detangler soaked baby-wipe all over her coat especially on the tangled spots. The baby-wipe works better than spraying the detangler directly on to the cat! Also you might try mixing a tiny bit of hair conditioner into a tablespoon or 2 of water and putting this directly on to the tangles, just use you fingers to apply it. But my favorite detangler is Frizz-ease hair serum. It's made with a silicone-based product and it's super slippery and removes knots in a jiffy! (look for the word "dimethicone" in the first word of the ingredients)
Also, my cat will only let me brush him while he is eating. So when he's super-hungry in the morning I always brush him while he's eating. It helps to offer wet food to get the cats attention. I keep a brush hanging up near his food bowl.
Start out grooming your cat with a wide-bristled brush at first, then after you've gotten out all the tangles, switch to a pet comb. (a small comb with about 1/4 inch spaces between the teeth) These combs will remove the hair that is shedding. You can also pet your cat with an old panty-hose on your hand and this will help remove some of the shedding hair. It's most important to brush your cat in the spring when they shed most!