I like this name and I think Mina is a cute nickname, but it might be too long for a child to spell. Consider that if you want to use this for your child.
Guillermina Candelario is a weightlifter from the Dominican Republic. She won three medals during her career at the Pan American Games (1999, 2003 and 2007) in the women's flyweight division (– 48 kg).
Guillermina "Gigi" Lozano is a Mexican-American geneticist. She is a professor at University of Texas MD Anderson Cancer Center. Lozano is recognised for her studies of the p53 tumour suppressor pathway, characterising the protein as a regulator of gene expression (transcription factor).
Guillermina Bravo (1920 – 2013) was a Mexican modern dancer, choreographer and artistic director of Ballet Nacional de Mexico. She was co-founder of the academy of Mexican dance (Spanish: Academia de la Danza Mexicana) in 1947 and established together with Josefina Lavalle the national ballet company in Mexico City in 1948, which has been located in Querétaro since 1991, where she also established the national center of contemporary dance. Bravo is considered as main figure of modern Mexican dance. Her sister Lola (1918–2004) was a notable stage actress.
http://www.ine.es/tnombres/formGeneralresult.do?vista=3
https://gl.wikipedia.org/w/index.php?search=Guillermina&title=Especial%3AProcurar&go=Artigo
https://gl.wikipedia.org/wiki/Lista_de_nomes_femininos_en_galego#F
(Information from name #31816 originally submitted by user bananarama)