Before going the legal route see if you can meet with her one more time. Go in knowing that you can’t budge on your fair price. Bring your estimate and labour details and material details. Some people respond very well to visually seeing differences, like price, laid out on paper. Compare the estimated labour with the actual labour and explain why you went over the estimate. Show her the materials you bought and explain that you HAVE to mark up materials because you pay interest on them. Offer to walk through the house to discuss the challenges you successfully met.
Lastly explain that you gave her an estimate and not a bid. In your area there is probably a percentage that a contractor can go over the estimate before expecting legal trouble being paid. You may want set up a monthly payment plan.
I’ve gone over budget on a lot of estimates, because I do very customized work, and have used this process to smooth over any bad relations. You did well to keep the client in the loop as you were going over your budget. Try to get her to see your point of view. You may not want to bring up a builder’s lien as that is the nuclear option.
One thing I changed in my business to become more assertive was to think of my family. When ever someone wouldn’t pay I’d view it as them stealing directly from my wife. If they wanted me to discount my work I’d imagine them taking a sum out of my kids college fund.
Follow the advice of some of the other comments on how to deal with this person who is taking advantage of your hard work.