In 2327, she graduated from Starfleet Academy with the rank of ensign. Along with her classmates, Jean-Luc Picard and Cortan Zweller, she visited Starbase Earhart to await her first deep space assignment. During her time there, she and the others got into a bar fight with some Nausicaans, in which she was knocked out and Picard stabbed through his heart. The incident resulted in Picard getting an artificial heart.
Picard and Batanides both had a crush on each other though neither decided to pursue it further. Picard later regretted that decision; however, when Q showed him what his life would have been like otherwise, he later came to realize that it would have meant the end of their friendship. (TNG: "Tapestry").
Marta Batanides was played by actress J.C. Brandy at the age of just seventeen.
According to the script for "Tapestry", her surname is pronounced "buh-TAN-ih-deez". She is also described as "a short, pretty woman, and is [...] roughly twenty-one." This would put her year of birth somewhere around 2306. 
Batanides has appeared in numerous non-canon works.
In the Star Trek: The Lost Era novel Well of Souls, Batanides meets Commander Rachel Garrett at Starbase Earhart, who is there awaiting transfer to the USS Carthage, where she will assume the position of first officer. The two women strike up a casual friendship, but they only meet each other for a couple of drinks at the local bar before they both go their separate ways. By 2336, she has risen to the rank of Commander, and has been assigned to Starfleet Intelligence. The criminal cartel, Asfar Qatala, becomes one of her major concerns after one of her operatives, Lieutenant Laura Burke, is captured and killed by a Qatala operative. The assassin then falsifies orders in Batanides' name in order to remove an officer from the USS Enterprise (NCC-1701-C). Fortunately, Batanides is able to contact Captain Garrett and the plot is foiled.
The Star Trek: Starfleet Academy comic Judgment, sees her promotion to Admiral in the year 2370, shortly after the recovery of the USS Pegasus. In 2373, she then serves on a tribunal to consider the punishment of Omega Squad after their unauthorized journey to the forbidden world of Talos IV.
The Star Trek: Section 31 novel Rogue states she has a special fondness for Andeluvian chocolate and 22nd century Earth "splitter" music. It also tells of her time at the Academy, where she becomes romantically involved with a Barangarian until his premature death. The relationship leaves her pregnant, and she soon falls into an irreversible coma due to Fetal Incompatibility Syndrome. Picard and Zweller then risk their careers to bring Marta to the black-market genetic labs on Yrskatdon, where she is cured by an illegal genetic procedure. In 2373, she becomes part of the Federation team sent to Chiaros IV to calm hostilities between the government and rebel factions, and to oversee a vote on whether the planet would join the Federation or the Romulan Star Empire. During the mission, her fiancé, Ambassador Aubin Tabor, is killed and revealed to be an agent of Section 31. With confirmation of this shadow group's existence, Batanides vows to bring it down.
Batanides appears briefly in the Star Trek: Destiny novel Lost Souls, during the Borg invasion of 2381. She is summoned to the Palais de la Concorde by Federation President Nanietta Bacco and Starfleet Admiral Leonard James Akaar, where she reviews reports on the progress of the Borg attack fleets.
Following this, in the Pocket TNG novel Losing the Peace, she is among several flag officers who attend a briefing by Captain Jean-Luc Picard regarding the absorption of the Borg Collective into the Caeliar gestalt.