In the Star Wars: Episode IV: A New Hope opening crawl, it says the Rebels won their first victory. The victory was in some battle that happened before the start of the film. From that battle, they retrieved the Death Star plans. What battle was that? Do we have any information on what happened during the battle?
The 'victory' referenced in the opening crawl did, indeed, occur just prior to the start of Episode IV.
A small team of Rebels headed by Jyn Erso and Cassan Andor infiltrated an Imperial data storage facility (located within a significant military base) while a number of other volunteers staged an assault.
During this mission, they were largely successful, managing to secure and transmit the plans for the Death Star to orbiting Rebel ships.
The 'victory' was a Pyrrhic one, as virtually everyone on the assault and infiltration force was captured or killed, and several starships were destroyed.
Prior to the new Disney movies and the exclusion of the novel canon to the new 'Legends' flag, this had been the canon answer:
The events are detailed in the novella "Interlude at Darkknell", which you can find in the book Tales of the New Republic.
The story features several people from Stackpole's X-wing series, several years before that series (obviously).
More info can be found at the Wookieepedia article on the plans.
The victory in question was, of course the encounter in which the rebels managed to steal the Empire's plans for the Death Star.
We get a little more info about this encounter in the newly-released (and Disney-canon) Star Wars novelisation for A New Hope: The Princess, the Scoundrel, and the Farm Boy.
Stealing top-secret plans from the Empire was a risk, but being dismissed as a twinkling ball of gas had only made her more determined. The mission should have been simple. All they needed to do was intercept a transmission about a new battle station the Empire was rumored to be building.
But the system had been swarming with Imperials. They’d caught on to Leia’s bogus tale about her ship’s breaking down, but the cover had helped her stall long enough to download the technical plans for something code-named “Death Star.” Despite the Rebels’ efforts to lose the Imperials in the jump to hyperspace, the hulking Star Destroyer had caught up to them. And Leia knew, the moment the ship identified itself as the Devastator, there would be no escape.
Moving down the canon scale, the battle is referred to as the "Battle of Orron III" in the Star Wars: X-Wing game, however it remains to be seen whether this will be incorporated in the upcoming Rogue One film which will act as a direct prequel to the events leading up to A New Hope and will detail the daring scheme to steal the plans for the Death Star.