Oswald Cobblepot of Earth-43 was, like in many realities, the villain The Penguin and an adversary of Batman, who had become a vampire.
The full details of the Penguin's earlier history are unknown, but it would appear that he and Batman had fought before, his murders apparently focusing on policemen.
Some time after Batman's 'disappearance', the Penguin broke out of prison, forming a gang to kill various cops. On the night that the now-vampire Batman was restored to life by Alfred removing the stake, Penguin was organising a trap for some cops that he apparently particularly hated in a warehouse district, stabbing one cop in the head with his sharp umbrella (the point going into his opponent's chin and out the top of his head) before Batman arrived, the shock of his appearance giving the cops the chance to escape. Although Penguin attempted to assert his confidence, protesting that it took more than some cheap trick to scare him, Batman retorted that he was the trick to Penguin's treat before effortlessly knocking the umbrella out of his hand and proceeding to tear Penguin's throat out with his teeth. Batman then began questioning Penguin's associates for the location of the rest of their gang.
Commissoner Gordon later noted that Penguin's head, along with the heads of those gang members who'd been present in the warehouse ambush, were found three miles from their bodies, Batman having taken their heads after he killed the criminals in order to prevent them returning as vampires.
Like many of Batman's foes in this dark reality, Penguin was more twisted in appearance, his exceptionally short stature belied by his use of sharp weapons.