The Gemara records a debate between Rav and Rav Assi as to whether it is permitted to read the Megila without a Minyan. Rashi and Tosafot clearly rule in accordance with Rav, who does permit it. The Shulhan Aruch (690:18) states that while ideally, one should seek a Minyan to read the Megila, it is permissible to read it alone.
When reading the Megila without a Minyan, the three Berachot prior to the reading are recited. However, there is a Machloket as to whether the Beracha of "HaRav Et Rivenu" is recited after the reading. The Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909), calling this Beracha very precious, rules that one does recite it without a Minyan. Hacham Ovadia, citing the Talmud Yerushalmi, vehemently opposes the Ben Ish Hai’s ruling. He holds that not only should one not say this Beracha, but, he should even not answer Amen to someone who does. Hacham Ben Sion adopts a middle position, finding basis for both positions, and allows a person to choose.
To avoid doubt in Berachot, one should not make the Beracha of "HaRav Et Rivenu" when reading the Megila without a Minyan. It should be noted that in this context, women and children who have reached the age of Chinuch also constitute a Minyan for the purpose of reciting this Beracha. Therefore, if a man reads the Megila for a group of women, he should recite the Beracha.
If one read the Megila without a Minyan, he should not recite the final Beracha of "HaRav Et Rivenu."