worked freelance bookkeeping for architect, refusing to pay my last invoice. said i didn’t do a good job since it cost her more in taxes

The issue isn't whether she "liked" your bookkeeping, or even whether it cost her more in taxes--the issue is simply whether you (1) did what you were contracted to do; and (2) followed proper bookkeeping standards and practices in doing it. If you did your job properly, even if the outcome wasn't what she hoping for, then she needs to pay you--that is, as long as there wasn't some sort of  a "guarantee" that you made (for example, that she'll owe less taxes if you do her books) that she can offer up as a reason to not pay.

Did you have a written agreement with your client? Did it spell out your duties? Was there some sort of written estimate for the hours you expected to work, or if not, are those hours in line with either industry guidelines or the hours you've billed this client or similar clients in the past? The more written evidence you have, the stronger your case; and conversely, without "back-up," it can turn into a "he  said, she said" kind of situation, in which you have difficulty proving what you're owed or that you did the proper job.

That said, let's assume you did what your client contracted you to do, and that you did it according to good bookkeeping standards. Let's also assume that your hours were reasonable and you can prove that. As stated above, your client owes you for the work done, period end of sentence. It is a contract and if you fulfilled your terms, she has to fulfill hers and pay you. She obviously has the right to not employ you in the future, but that's a different story.

However, that said, if you client refuses to budge, you have to weigh the cost of trying to collect--which may mean hiring an attorney--versus the additional amount (the amount over the 1/2 she's offering) you hope to get. You also need to consider the distraction to you of fighting with a client, the potential bad publicity or word of mouth. You might decide that settling for less than full is the right thing to do...for example, suppose you got her to pay 3/4 of what was owed--would that be worth it, to get the money and move on with hour life and business? Regardless of your legal rights, you need to ask yourself that sort of practical question.