Nissim was born in the Jerusalem neighborhood of Ohel Moshe on February 2, 1928 to a well-established Sephardic family. His father, Eliyahu Yifrach, owned a store in the commercial center which was burned down by Arab rioters after the Partition Plan was announced. His mother Rachel died while Nissim and his sister were still young. His grandfather was Rabbi Benzion Cuenca, chief rabbi of Hebron and head of the rabbinical court in Jerusalem.

Nissim studied in the Alliance school, continuing in Terra Sancta High School, but he had to leave his studies. He first worked for an accountant named Broyde, then the lawyer Pinchas Rabinowitz. In 1945, he joined Lehi in Jerusalem. He was injured and arrested when putting up posters, for which he was put on trial and imprisoned in Latrun, where he remained until the British left. On 15 May, 1948, he returned to Jerusalem and to operational status at Mahane Eldad, the Lehi camp in Lifta. He fought the Arabs in battles around Jerusalem. In September, he enlisted in the IDF, serving in Battalion 68 of the Jerusalem Brigade and completing a communications course. As a reserve soldier, he fought in the Sinai War in 1956.

After the War of Independence, he was among the Lehi members who formed the core of Neve Yair along the Gaza border. This group broke up, but Nissim was still inspired to try again. After agricultural training in Mikve Israel, he went in 1955 to settle Nir Banim near Kiryat Gat.

The same year he married Ziona Razhabi, a teacher, and they had two daughters: Rachel became a social worker and Nili worked at Ministry of the Interior. Nissim was the brother of Rut Yahalom and brother-in-law of Yaakov Yahalom, all members of Lehi.

After some time, he came down with a severe kidney condition and, under medical advice, had to give up his agricultural career. In 1961, he moved to Ashdod and started working at a nuclear research facility in Nahal Sorek, until his death on November 25,1974. While working there, he pursued studies in mathematics and English and even discovered talents in painting and craftsmanship.