Make sure you use a good name brand nail polish remover like Sally Hansen or Cutex and that it has Acetone in it. The non-acetone is good for fake nails but it won't remove the glitter.
If you're having trouble with cotton, try using something with abrasion in it like the sponge backs of dish sponges that have a little scratch to it. But if you use the right remover, you shouldn't have a problem. Unless you have fake nails. If you do, use the Acetone, just don't leave it on too long or it melts the acrylic.