The following article contains spoilers from DC vs. Vampires: All-Out War #3, on sale now.
The origin of how Nightwing became a vampire has finally been explained in "Dark Birth: Part 2" from DC vs. Vampires: All-Out War #3 (by Emma Vieceli, Haining, and Troy Peteri). Nightwing was forcibly turned by a vampire named Pandora. She wanted to use him as a weapon against the then vampire queen to restore power to her faction of vampires, who saw themselves as superior to humanity. After a lengthy fight against multiple vampires, Nightwing was finally turned.
What came after though was incredibly shocking. Nightwing not only killed Pandora immediately after being turned but seemed suddenly onboard with the idea of confronting Mary. It seems like he gave up far too quickly. Yes, technically he is now undead, but he's also seen other, far more impossible things happen. Rather than give in to his new state of existence, he could have tried to fight it, ask for help, or do any number of things that didn't involve taking over the world.
It doesn't seem to be in Nightwing's nature to give in -- at least not easily. Yet, he did so multiple times throughout the issue. He gave up when surrounded by vampires, he acquiesced to Pandora's wishes to confront Mary, and he even turned his back on Batman's "no kill" rule. Overall, this issue showed Nightwing at his weakest emotionally, succumbing to multiple influences. However, the biggest mystery is what happened after he became a vampire. He didn't want to be turned, and nothing was said to convince him to willingly join their cause. Nightwing suddenly murdering Pandora indicates that some part of him wanted to fight back, but nothing reveals what caused his shift in loyalty
One possibility is that becoming a vampire might have made him believe what Pandora said -- that vampires are better than humans. Since Pandora was apparently the strongest among them but she still turned to Nightwing for help, it may have triggered a little power trip. It could have been like taking a drug -- getting high on the strength he suddenly possessed and agreeing that they deserve to be at the top of the food chain.
Another possibility is that, in his new state, he recognized that there was little that could be done to save him. Vampirism is a mystery in the DC Universe. So much so that curing it may seem impossible to him. With that in mind, Nightwing would likely have no choice but to commit to his new species, and try to improve their lives because that's just the kind of person he is. Still, it seems odd that in a world of resurrection, aliens, and gods, he never once contemplated trying to undo what has been done.
There are multiple means of coming back from the dead, surely one of them might be able to fix this. Instead of trying, he immediately latched on to the idea of vampire supremacy. Giving him the benefit of the doubt though, maybe Nightwing wasn't fully onboard with the plan for conquest yet. He only asked to speak with Mary, he never stated he would kill her. Perhaps he wants to know if there is a way to reverse the change. Regardless of his intentions though, it's clear what path he chose to walk down.