The full expression (at least in the Spanish-Portuguese custom) is "hazaq ubarukh tihye" (yes, that "b" is beth without daghesh, as is standard in Spanish-Portuguese Hebrew pronunciation).
The challenge is that we do not know whether it is "be strong (verb) and be blessed" or "be strong (adjective) and blessed". In the former case, the heth would have the vowel hateph-pathah. In the latter case, the heth would have the vowel qames. In the former case, the feminine would be "hizqi ubrukha tihyi" (or briefly, "hizqi ubrukha"), while in the latter case the feminine would be "hazaqa ubrukha tihyi" (or briefly, "hazaqa ubrukha").
In Spanish-Portuguese custom, the response to "hazaq ubarukh" is "barukh tihye" (which is also the Ashkinazic response to "yashar kohekha"). In the Mizrahi custom, however, the response is "hazaq we'emas" (Joshua 1:6, Deuternomy 31:7). In the response, hazaq is certainly a verb, which might suggest that it should be a verb also in the "hazaq ubarukh". I have read (apologies that I don't have the reference), that the first indication of such a custom said that people would say only "hazaq", which suggests that it began as the verb.
I think the preponderance of the evidence is that the phrase began with "hazaq" as a verb, which would indicate we should say to a woman, "hizqi ubrukha". However, whenever I have heard it in actual use, what was said was "hazaqa ubrukha". I conclude from this that over time hazaq became understood as an adjective rather than a verb, and it is now so understood by the user community. Thus, "hazaqa ubrukha" seems the most appropriate phrase.
"hazaqim ubrukhim!" to you all.