This is a Batman (Jason O'Mara) trilogy of animated movies which tell the story of Batman's son Damian/Robin (Stuart Allan) Damian's mother, Talia (Morena Baccarin), and Nightwing (Sean Maher) who previously was Robin but outgrew the costume.
In the movie Batman's son is living with his mother and grandfather. Ra's al Ghul (Giancarlo Esposito) at a monastery, League of Assassins. Deathstroke (Thomas Gibson) and his men attack the monastery, leaving it in ruins and killing al Ghul. Mother then brings Damian to Batman to care for him for a time.
In "Batman vs. Robin" Talon (Jeremy Sisto) plays a large part; especially in turning Damian/Robin against his father. He is working with a group called Court of Owls. However in the end he betrays the court as he is actually working on a way to create immortality, so people can regenerate. He uses these as his minions. Robin was actually going to join Talon, but he realizes he is still loyal to Batman and the thought, justice not vengeance. Leads to a large battle at the end, including Batman, Robin and Nightwing, and even Alfred (David McCallum).
Finally in the last movie, Bad Blood, we are introduced to two more characters, Batwoman/Katherine Kane (Yvonne Strahovski) and Batwing/Luke Fox (Gaius Charles). Batman wants to keep the fighting inside the family, meaning he and Robin and Nightwing. However without the help of others they would not have survived. Infact Batman is taken captive, and Nightwing and Robin cover for Batman. They eventually rescue him, but he has been brainwashed with the use of a trigger. The same trigger has been put in many prominent people. It is Damian's mother who is actually wanting to control the world as leader of the League of Assassins.