He later studied at the College Josefino in Saltillo and, around 1865, moved to Mexico City, where he became a boarder at the Colegio de San Ildefonso.

From here he was transferred to a room at the medical school, the same one that some years before was inhabited by another Mexican poet, Juan Díaz Covarrubias.

In the same year, encouraged by the cultural renaissance that followed the triumph of the Republic, he participated, along with Agustín F. Cuenca and Gerardo Silva, among others, in the founding the Nezahualcóyotl Literary Society, in which he presented his first verses.

Her house was frequently turned into a social gathering place for these poets, where each one exposed his new verses and debated philosophy.

It is said that tears welled up in his closed eyes, in accordance to advice given in a poem that he wrote: "como deben llorar en la última hora, los inmóviles párpados de un muerto" ("As the immovable eyelids of a dead man must cry in the last hour")[2] His unrequited love for Rosario de la Peña was said to be the motive for his suicide.

On December 10, Acuña was buried at the cemetery “Campo Florido”, with the attendance of representatives of literary and scientific societies, as well as a huge crowd of people that admired him.

His best friend Juan de Dios Peza, Eduardo F. Zárate and Justo Sierra gave their last goodbyes to Acuña.

In 1890 his body was transferred to the Rotunda of Illustrious Persons (Spanish: Rotonda de las Personas Ilustres), where a monument was erected in his honor.