Zúñiga was born in Guadalupe, Barrio de San José, Costa Rica on December 27, 1912 to Manuel Maria Zúñiga and María Chavarría, both sculptors. His father worked as a sculptor of religious figures, and in stone work. His artistic inclinations began early and by the age of twelve had already read books on the history of art, artistic anatomy and the life of various Renaissance painters. At age fifteen he began working in his father’s shop. This experience sensitized him to shape and spaces. In 1926 he enrolled in the Escuela de Bellas Artes in Mexico, but left the following year to continue on his own. As part of his self-study, he studied German Expressionism and the writings of Alexander Heilmayer, through which he learned of the work of two French sculptors, Aristide Maillol and Auguste Rodin, coming to appreciate the idea of subordinating technique to expression.
Zúñiga’s painting and sculpting work began receiving recognition in 1929. His first stone sculpture won second prize at the Exposición Nacional de Bellas Artes. In the following two years continued to win top prizes at this event. This work made critics recommend him for study abroad. He won first prize in a 1935 Latin American sculpture competition, the Salón de Escultura en Costa Rica, for his stone sculpture La maternidad, but the work caused controversy and the government rescinded its award. In the 1930s, he began to research pre Hispanic art and its importance to contemporary Latin American art, as well as what was happening artistically in Mexico. The scholarship never materialized so various colleagues organized his first individual exhibition in Costa Rica. The earnings from this endeavor earned his passage to Mexico City. In 1936 he immigrated to Mexico permanently
In the capital, his first contact with Manuel Rodríguez Lozano, who opened his library to Zúñiga. He did some formal study at La Escuela de Talla Directa, working with Guillermo Ruiz, sculptor Oliverio Martinez, and painter Rodríguez Lozano. In 1937 he worked as an assistant to Oliverio Martínez on the Monument to the Revolution, the re-imagined building that had begun as the Federal Legislative Palace conceived during the regime of Porfirio Díaz. In 1938, he took a faculty position at La Esmeralda; he remained at that position until retiring in 1970. In 1958 he was awarded the first prize in sculpture from the Mexican National Institute of Fine Arts.
In the 1940s, the New York Museum of Modern Art acquired the sculpture Cabeza de niño totonaca and the Metropolitan Museum of Art requested two of his drawings. He also helped to found the Sociedad Mexicana de Escultores and received commissions in various parts of Mexico.
In 1949, he was part of the founding board of the Salón de la Plástica Mexicana, and in 1951, he joined the Frente Nacional de Artes Plástica of Francisco Goitia .
Major individual exhibitions during his career include the Bernard Lewin Gallery in Los Angeles in 1965, a retrospective at the Museo de Arte Moderno in 1969 and various exhibitions in Europe in the 1980s.
In 1971, he received the Acquisition Prize at the 1971 Biennial of Open Air Sculpture of Middelheim in Antwerp, Belgium. In 1975 twenty of his drawings with the Misrachi Gallery obtained the silver medal at the International Book Exposition of Leipzig. In the 1980s, he was named an Academic of the Accademia delle Arte e del Lavoro in Parma, Italy. In Mexico he won the Elías Sourasky Prize.
In 1984 he won the first Kataro Takamura Prize of the Third Biennial of Sculpture in Japan.
He became a Mexican citizen in 1986, fifty years after his arrival in the country.
In 1992 he received the Premio Nacional de Arte, and in 1994, the Palacio de Bellas Artes held a tribute to his career.
Near the end of his life, illness left him nearly blind, which caused him to shift his artistic work to terra cotta, using his hands to create the lines