While an undergraduate student at George Washington University (A.B.1920, M.S. 1921), she worked for the War Department and became Aide in the Division of Herpetology at the United States National Museum. Although the museum was under the curatorship of Leonhard Hess Stejneger, Cochran was responsible for the administration of the herpetological collections. In 1927 she became Assistant Curator and in 1942, Associate Curator just prior to Stejneger's death. She earned a Ph.D. at the University of Maryland in 1933 with a thesis on blue crab myology. She became the first woman Curator in 1956 until her retirement in 1968 on her 70th birthday.
She studied art at the Corcoran Art School and developed her talents as an artist, becoming a scientific illustrator not only for her own works, but also for those of her colleagues.
Cochran's research was focused primarily on the herpetofauna of the West Indies and South America, particularly Brazil and Colombia. She published 90 taxonomic papers between 1922 and her death (four days after her retirement in 1968) in which she described 8 new genera and 125 species and subspecies as well as wartime booklets for the military identifying venomous reptiles. Her 20 years of studies of the West Indies culminated in The Herpetology of Hispaniola in 1941.
She went on to write mostly about South American frogs in Frogs of Southeastern Brazil in 1954 and Frogs of Colombia in 1970 (posthumously). Her most popular book was Living Amphibians of the World in 1961. Cochran personally collected over 3,000 frogs in an expedition to Brazil.
Cochran was the second person to be elected a distinguished fellow of the American Society of Ichthyologists and Herpetologists.