There are two types of Hallel that we recite on special days during the year. There is the full Hallel, which has a Beracha (blessing) before and after and includes all of the paragraphs of Tehillim from Mizmor (psalm) Kuf Yud Gimel 113 to Mizmor Kuf Yud Chet 118. Then we have what is called Chatzi Hallel, half Hallel, which is recited on Rosh Chodesh (new month) and on Chol HaMoed (intermediate days of the festival) Pesach. This omits the Beracha before and after and skips select passages within those Mizmorei Tehillim.
On the holiday of Hanukkah, for all eight days, we recite a full Hallel with a Beracha before and after to remember the great miracles that Hashem performed for us with the war and with the candles, as we do on many other yamim tovim (festival days). If a person mistakenly recited the half Hallel without a Beracha and without the added passages, they would have to repeat the Hallel with a Beracha before and after and all of the passages to fulfill their obligation.
If a person made the Beracha before and then, for whatever reason, skipped the paragraphs as if he were saying half Hallel, then he must go back to the beginning and recite the paragraphs in order, from Kuf Yud Gimel to Kuf Yud Chet, without reciting the passages out of order. He cannot just insert them, because anybody who recites the Hallel out of order does not fulfill their obligation. They do not have to repeat the Beracha because the Beracha they said still counts, but they have to go back to the beginning, recite the passages in order, and then conclude with a Beracha. If a person began the Hallel without a Beracha, then whenever they remembered that they had not said a Beracha, they could insert the Beracha in the middle, then continue and conclude with the Beracha. That is provided that they said all of the passages as though it were a full Hallel. If a person, however, said the entire Hallel—all of the passages—without a Beracha before, they would not say the Beracha at the end, and they would not go back and repeat the Hallel. They fulfilled the obligation without the Beracha. If a person is unsure, however, whether he read the Hallel, then by law, he does not have to go back and reread, but it is appropriate for him to go back and read without a Beracha.