It sounds really awkward. So, I'd say that it grammatically, has a mistake. Tired she was -- This sounds awkward and normally does not stand on its own. We normally use "She was tired." In this the noun must be first when describing a pronoun like she. You may say: "She was tired, but she still carried on." "Even though she was tired, she still carried on." They both mean the same thing. If you have any questions, just ask :))

I think that what you are trying to say is : As tired as she was, she still carried on

There are NO grammatical mistakes in the sentence. The form is not used in normal conversation though.