Question: It is not always easy for me (a woman) to make it to shul to hear Parashat Zachor. How much of an effort must I make?

Answer: There is a mitzva from the Torah to remember the actions of Amalek. It is related scripturally and, as simple logic dictates, innately to the mitzva to fight them (see Devarim 25:17-19). According to some Rishonim, it is included in the latter mitzva – see Mikraei Kodesh, Purim 5.) The question of how and when the Torah prescribes the mitzva can influence whether a woman has an obligation.
The basic mitzva of remembering can ostensibly be done at any time, which seems to preclude an exemption for women on grounds of being a time-based mitzvot. That which we do it on a specific Shabbat is Rabbinic. Yet, for a long time, the minhag was that women did not come to shul like men to hear Parashat Zachor, which prodded poskim to look for a reason why.
The connection to the mitzva to fight could be significant in this regard. One claim is that battle is usually carried out in the day, making it time-based. One of several questions on this idea is that one can remember the need anytime and act when it is practical. The Chinuch (#603) says that since women as a group are not obligated to wage battle, they are not included in the mitzva to remember either. The Minchat Chinuch (ad loc.) argues with the Chinuch by poignantly pointing out that women can and often should take part in other war-related efforts (see Sota 44b). Others argue that mitzvot are not dependent on whether the mitzva’s assumed logic applies to an individual. On the other hand, the Chinuch’s logic is reminiscent of the halacha that Moavite women are not included in the prohibition on marrying into our community because they do not usually bring provisions to nations passing through. Due to the Chinuch’s stature and the old minhag, it is hard to discard the opinions that women are exempt.
It is also possible that women, while obligated, fulfill the mitzva in other ways. The gemara (Megilla 18a) derives that the remembering of the story of Amalek should be done through a recitation from a sefer. The Terumat Hadeshen (I:108) posits that reading Zachor from a sefer Torah with a minyan is required from the Torah. Regarding men, we accept this opinions, thus making us expect men to go to significant lengths to have a minyan for Shabbat Zachor (Shulchan Aruch, Orach Chayim 685:7). However, not all agree that Torah law requires a minyan and perhaps not even a kosher sefer Torah. If so, the Rabbinically prescribed way men fulfill the Torah law (Shabbat Zachor), which is time-based, may not be binding for women (see Torat Chesed, cited in Yechaveh Daat I:84; Mikraei Kodesh, ibid.). If women have an obligation for some type of remembrance but not necessarily like men, it is not surprising that some (including Teshuvot V’hanhagot II:344) say that they should take the opportunity of Shabbat Zachor to read those p’sukim from a Chumash.
There is another possible way for women to fulfill the mitzva, which, if correct, does not require an extra action. Some Rishonim say that it is possible to fulfill the mitzva of Zachor by listening to Megillat Esther, which women anyway must do and usually even have a minyan (see Teshuvot V’hanhagot ibid.). It might just be necessary to have in mind for Zachor during that time (ibid.).
In general, over the last few hundred years, the minhag has developed for women to try to make to shul for the reading of Parashat Zachor (see Binyan Tzion (Chadashot 8) in the name of Rav Natan Adler). When this is doable, it is a good thing. However, if one has difficulty doing this, she should not feel undue pressure, and can rely on the several opinions and the old minhag that she does not have to fulfill the mitzva the way men do (Yechaveh Da’at, ibid.). (Some communities have a second reading. There are different ways of doing this, which raise certain halachic questions (see Minchat Yitzchak IX:68). However, whatever system a community uses should be fine for the individual who wants to hear.)