Late last year we had heard rumors that Nightwing may appear in the film after having a "falling out" with the Caped Crusader. We don't know if this back story has been written out of the current script by Chris Terrio but according to Badass Disget sources a Robin Shire will be present in the film featuring a dead Robin. Also goes onto say that Batman is nothing more then an urban legend by the start of the film:
"My sources indicate that when BvS opens Batman has existed for close to thirty years, which would place Wayne in his 50s.. In this version Batman is still an urban legend, a creature of the night, and no one has ever taken his picture. But he's had plenty of adventures, and the Batcave includes a memorial centered around a tattered Robin costume. He's a quieter operator (Unlike Bale's Batman), not involved in blockbuster battles but in all sorts of badass vigilantism."
It's highly unlikely DC will kill off the first robin Dick Grayson off-screen when he could be used in future films. The most likely candidate is Jason Todd the second Robin who is beaten to death by The Joker but comes back to life as the Red Hood. This could set up a Red Hood story line in The Batman solo film starring Ben Affleck. As a fan casting for Red Hood/Jason Todd a good choice would be Need for Speed and Breaking Bad star Aaron Paul!
Of course this is all a rumor until proven otherwise...
Batman v Superman: Dawn of Justice hits in 2016