The daughter of an attorney and an elementary school teacher, Robledo was born in Edinburg, Texas and lived there until she was 15.
Her love of performing began early when, at the age of 2, her parents took Robledo to the ballet. According to her parents, she was dancing in the aisles and begged them to sign her up for classes.
Robledo earned a BFA in Acting from the Conservatory of Theatre Arts & Film at SUNY Purchase.
Her earliest acting credit came from the short film, Kitsch.
Robledo rose to prominence in television with the show Gossip Girl in 2009 as Amalia.
Her film credits include small parts in What Happens in Vegas, Going the Distance and The Escort. Her other short film credits include the co-produced The Banana Runt People, Grrl Scouts, Last Tuesday of Driving, Matt & Kevin Retire From Being Superheroes and And After which she also co-produced and co-wrote.
Aside from acting, she also acted as a producer for the 2015 TV series, Beautiful Fools.
Her television roles include Agent Carter, episodes of Beautiful Fools, and as Skyler on Interns of F.I.E.L.D.