How do I get legal power of attorney for a parent with dementia?

You can't

You can't get a POA from a person with dementia. You see a lawyer and you pursue a Guardian or Conservator appointment in court.

I agree with Windyridge above, your parent would need to be able to understand the wording in a Power of Attorney. Attorneys will refuse to have someone sign if that Attorney feels the person isn't competent.

Your parent must be judged mentally competent to assign a POA. It doesn't sound like they are. You may want to look into legal guardianship.