In 1608, he was employed as interpreter by the viceroy, which appointment he owed to his learning and skill in explaining the hieroglyphic pictures of the ancient Mexicans.
In spite of his illustrious birth, good education and obvious ability, he lived most of his life in dire poverty.
He gives a detailed account of the important part played by his great-grandfather Don Fernando Ixtlilxóchitl II in the conquest of the Aztec Empire and the pacification of the Indigenous of New Spain, praising him in every possible way and condemning the ingratitude of the conquerors.
Later (1610 to 1640, according to Chavero), Alva wrote the Spanish work Historia chichimeca, which refers to the same events, but with more organization.
Historia chichimeca is not the original title, which is unknown, but was supplied by Carlos de Sigüenza y Góngora when the manuscript was in his possession.
Lorenzo Boturini Bernaducci, who owned the same manuscript later, called it Historia general de la Nueva España.
His works contain very important data for the history of Mexico, but except for Historia chichimeca, they are written without order or method, the chronology is very faulty, and there is much repetition.
He wrote two memorials, Sucinta and Sumaria, addressed to Viceroy Luis de Velasco, hijo, and Fray García Guerra.