Some TMNT stuff really isn't for little kids.
Prior to the events of the Batman/Teenage Mutant Ninja Turtles miniseries, Damian Wayne was overseas monitoring the League of Assassins. When he returned, he found Michelangelo, Donatello and Casey Jones playing video games in the Batcave, and attacked them. The conflict was interrupted by Batman's return, and Damian revealed that the League was converging on Gotham City.
He accompanied his father to Arkham Asylum in order to stop the Shredder and Ra's al Ghul, but they were greeted by a number of criminals and inmates who had been mutated. When Batman was frozen in place by Mr. Freeze, Robin left the facility in order to disarm the League's assassins and deliver them to the GCPD.
Several hours later, he expressed sympathy for his father on the anniversary of his parents' death, and the two decided to spend time working on the Intimidator suit together.
In Batman/Teenage Mutant Ninja Turtles II, Robin accompanied his father on a mission to discover the truth about a mass breakout at Arkham Asylum. They quickly discovered that the League had a new leader, and that there was a Lazarus Pit underneath Gotham. The two rushed to the site, fighting Ninja Man-Bats along the way, but were too late to stop Bane from using the Pit. However, before they could engage him, Donatello's multiversal teleportation system accidentally exchanged Bane for the Turtle.
In order to create another such device, Robin and Donatello had to obtain a machine part from Mr. Freeze; with Donatello's technical skills, they succeeded. He accompanied his father to the Turtles' home dimension, where he revealed Donatello's part in the city's chaos to the other Turtles.
He was left with Raphael, Donatello and Michelangelo while Batman was on a mission. But his continual contempt for them—and in particular for Donatello—angered Raphael into fighting the young boy, until Batman intervened. He later accompanied his father and the Turtles into Bane's stronghold, only to face Venom-infused Bebop, Rocksteady and Foot Ninja. He sparked off the conflict by attaching a bomb to Bebop's arm.
His hostility towards Raphael was tempered with compassion after Splinter was badly injured. He accompanied them to the Lazarus Pit in his home dimension, and fought the Ninja Man-Bats after Splinter was healed. He then accompanied Nightwing and the Turtles in the Turtle Van, and fought Rocksteady, Bebop and Bane. After Bane's defeat and capture, he then accompanied Nightwing, Batgirl and his father to their home dimension.