To become UC eligible, you need to fulfill the requirement by high school courses, college course, or AP/IB credit as described here: University of California - A-G courses
There is also eligibility by exam, as described here: University of California - Admission by exam
There is also eligibility by exception, as described here: University of California - Admission by exception
However, do not be surprised if the latter two methods result in a lower chance of admission than if you were eligible the usual way by fulfilling a-g requirements.
You do realize that UC financial aid will not cover the $22,000 additional out-of-state tuition, right? (see the financial aid estimators on their web sites)