Are women required to recite full Hallel with a Beracha (blessing) before and after? To answer this question, we usually go to the concept of mitzvat aseh, a time-bound positive commandment. Celebrating Hanukkah and reciting Hallel during this time of year would certainly fit that. Usually, women are exempt from such a thing.
The problem is that on Hanukkah, the Chachamim (the Sages) obligated us to light the candles. They included women in the obligation to light the candles because women were also included in the decree and in the salvation. So women have an obligation to light the candles just like men, and in many cases can even light on behalf of men. Once women were obligated to light the candles, it would seem that the Chachamim would also obligate them to recite Hallel with a Beracha before and after.
Some said, no, there is a difference. When it comes to reciting Hallel, even for a de-rabbanan (rabbinic) holiday like Hanukkah, the recitation of Hallel is mi-de'oraita, it's from the Torah. How did they argue that? They said that even though the holiday is created by the rabbis, the rule is that we learned from a precedent in Yetziat Mitzrayim, from the shira that they sang on the sea: Any time a great miracle is done, if the Chachamim determined it should become a holiday, then from the Torah you're obligated to say Hallel, as you are on Sukkot, on Shavuot, and on other holidays.
Many of them said that, no, the obligation for Hallel is from the Torah. Therefore, the Torah always exempts women from a mitzvat aseh shehazman gerama, even when they participated in the miracle. The rabbis only have the ability to obligate women in Hallel when it's fully de-rabbanan, or in any mitzvah (commandment) when it's fully de-rabbanan. Which Hallel is it? It's de'oraita, and therefore they would be exempt. Only in lighting the candles and reading the Megillah, which is de-rabbanan, would they be obligated.
The problem with this is that most poskim (halachic decisors) don't hold this way. The Rambam and others hold that reciting Hallel is de-rabbanan, and yet they still exempt the women. So how do they do this? They make the distinction that lighting the candles is for pirsum ha-nes. It's the publicity of the miracle. Women are obligated to publicize the miracle because they were included in the miracle. Hallel is not publicizing the miracle. It's giving gratitude for the miracle, and in the gratitude, the Chachamim did not obligate them. Whereas in the publicity of the miracle, they did obligate them.
Therefore, even though they're obligated to light the candles, they're not obligated to recite Hallel. If they wish to say Hallel, they may do so, but they cannot make a Beracha before and after. This applies to Sephardiyot (Sephardic women). Ashkenaziyot (Ashkenazic women), who have the custom that whenever they perform their mitzvah voluntarily, they can make a Beracha, have the right to say the full Hallel with a Beracha before and after. Have a great day.