WARNING: The following article contains spoilers from Robins #3, on sale now from DC Comics.
The First Robin has finally made herself known to Tim Drake, who was one of several to wear the mantle after her. However, despite capturing him and torturing him, it would seem that her ultimate goal is not to kill the Robins, but instead to break Batman. Instead of physically punishing him though, the First Robin seems intent on turning his partners against him, trying to slowly sway them to her way of thinking in regards to their relationship with the Dark Knight, and she is showing surprising success in doing so.
At some point during a fight with the Junior Supercriminals in Robins #3 (by Tim Seeley, Baldemar Rivas, Romulo Fajardo Jr., and Steve Wands), the First Robin abducted Tim Drake, taking his identity by using the same physically altering tech that the villains were using. The goal was to sow discord, not by making the Robins lose the fight, but by taking away their unity.
Disguised as Tim, the First Robin ignited an altercation with her counterparts. She pretended to be willing to fight them, knowing the other Robins would not stand for this, thus driving a wedge between the adoptive siblings. Her conviction in sowing this mayhem was so strong that she even took a solid hit from Red Hood, being knocked out in the process.
Surprisingly enough, her plan turned out to be a success. In the aftermath of the fight, Nightwing was so angered by Batman's lack of concern regarding Tim that he outright stated that being Robin was never a good thing, wounding Batman in a way no supervillain ever could.
This turned out to be the First Robin's goal all along. As she returned to a captive and beaten Tim, she remarked how she could understand why they would stand alongside Batman. Each of them admired what he stood for, but she also knew that there were weaknesses to exploit. The cracks in the Robins' relationships with the Dark Knight have now been exposed, pushing old resentments to the surface and hurting the Caped Crusader in a way no physical blow ever could. It seems that the First Robin's goal is to make her peers feels the same degree of animosity she feels towards their mentor.
This is supported by the fact that, despite having had Tim in her power all this time, she hasn't killed him. The First Robin took the opportunity to hurt him, but she refrained from going too far. This shows that her vendetta is against Batman, and she wants to condemn him for turning them all into soldiers in his personal war, and based on how easily she managed to divide the Bat-Family, she appears to be succeeding. By turning the Robins against him, she not only gets her revenge, but also robs Batman of his very legacy.