In 52 she's introduced tossing a human through the air while crushing the jaw of a mutant fish-faced crocodile creature, inflicting an injury that "the Batman himself would think twice about before inflicting." That is not a quote from a fanboy or reviewer, but of an actual comic author who has written Batman.
In Batwoman #0, after being ambushed by Bruce Wayne in disguise as a Secret Test of Character, she kicks him in the face and makes him bleed. Sure it was a set up, but it was still awesome.
Kate, feeling like everything is pointless, completely lost and without a purpose in her life... looks up into the sky and sees the Bat Signal, and realizes that's her purpose. One can almost hear the Danny Elfman Batman theme swelling to a haunting crescendo during that bit.
Her final battle against The Weeping Woman has Kate literally confront her demons and come to terms with her sister's death.
Medusa's completely invaded Gotham and is basically unleashing hell when Batwoman returns to Gotham with Wonder Woman in a Big Damn Heroes moment.
The Grand Finale that is issue #17, and which really should have been named "Batwoman Does Many Awesome Things." Among them, she defeats Medusa with her wits and battles hordes of monsters using only hand-to-hand combat. And remember those missing kids, the ones she's spent months searching for? She rescues every single one of them.
While she may not be on Batman's level, the glimpses of her training seen in Detective Comics, Secret Origins, and the 0 issue of her ongoing show she's no slouch, either. Highlights include learning to fight while blindfolded and handcuffed, catching arrows barehanded, crossing the Sahara Desert on foot with limited supplies, exposure and desensitization to various chemical agents, and undergoing various forms of torture.
Kate's Heroic Sacrifice in the form of her dismissal from West Point. After the deaths of her mother and sister, the only thing Kate ever wanted to do with her life was to serve in the military; however, this meant she had to keep her sexual orientation a secret, since Don't Ask, Don't Tell was still in place. While at West Point, Kate is accused of being a lesbian, and learns that she is the only one under suspicion at the moment. Realizing that a full investigation would not only expose her but her girlfriend as well (and possibly others), Kate declares she is gay and drops out from the school. She gave up the only dream she ever had to spare others and to remain true to herself, and she did so without hesitating.
In her first appearance in "DC Rebirth," Batman comes to her to ask her aid in training a new generation of crimefighters for Gotham. When she asks why, Batman unmasks to reveal himself as Bruce Wayne. To his shock, Kate laughs that "I've been waiting a year and a half for you to finally say it," revealing she's known her cousin was Batman for while now.
Just before this, she had another one. Batman had broken into her apartment in order to meet with her, and Kate sensed him in the shadows without him making a sound. She then snatched him and threw him halfway across her apartment over her head.
In DC Comics Bombshells Kate singlehandedly takes on Edel Nacht and an army of SS troopers backed up by Zombies, inspiring the entire Berlin Jewish Ghetto to rise up and resist being liquidated. That's right, Kate halts the start of the Holocaust!