Are women Halachically responsible to hear the reading of Parshas Zachor?
Chinuch 603 says women are not obligated in the active biblical mitzva of remembering what Amalek did, and in 605 says that the details of the "don't forget" mitzva were covered in 603, which Minchas Chinuch (in 603) says "seems a little" to imply that they're exempt from that one, too. However, MC himself (in 603) seems to decide that they are obligated in both the mitzvos.
Note, though, that besides the biblical mitzvos, there's a rabbinic enactment of reading the four parashiyos. I don't know the parameters of this obligation, but I'd assume that it's either on the tzibur as a whole or, at least, not on women.
Rabbi Menachem Greenblatt (St. Louis, Mo.) mentioned today that, although they should make every attempt to listen [and his shul has a second reading for them], women can rely on those who say they are exempt. I trust I'm quoting him correctly, but you're encouraged to ask him yourselves to be sure. As always, for practical halacha, CYLOR.