Arizona now has a legal method of emanicaption for minors. See question 18496

Original answer to question before the law was enacted:

Arizona has no legal method for having a court declare you emancipated.  Few people have been found by a court to be emancipated based on circumstances like you have described.  However, emancipation is often done as a result of a creditor trying to force a Minor to pay a debt created by a contract signed by the Minor before they were eighteen.  Contracts by Minors are usually unenforceable.

One option for you is to ask your parent or guardian to allow you to live on your own.  However, that parent or guardian would remain liable for your support, any needed medical care, and would need to sign authorization for medical treatment.  In other words, your parents would retain all their legal obligations to you.  A landlord would likely want your parents to co-sign on any lease, so the landlord could continue to receive rent from your parents in the event you can't make the payment.  

To be  cautious about such an agreement, all parties should speak with an attorney to be sure tax and other legal consequences are understood.  (Generally, a Minor's income counts for parents.  Your income could affect the taxes your parents pay to the IRS. )