Curaré was a member of the Society of Assassins, and its deadliest and most infallible killer.
Nobody knows Curaré's true identity, and nobody has seen her face (apart from Batman). But everybody knows she's deadly, and possessed an unending knowledge of killer tactics. She was an excellent martial artist, and was designed to kill. She possessed a scimitar that has an edge no thicker than a molecule. It could cut through anything and she often used it to deflect gunfire.
In the Society of Assassins, the price of failure was death, and Curaré was the first to run afoul of that rule when she finally met her match in the form of Batman and Barbara Gordon. Both of them, working together, managed to capture Curaré and saved district attorney Sam Young from her lethal blade. Curaré managed to escape, but then had to face the fatal consequences of her failure.
She, however, managed to turn the tables on the Society of Assassins, hunting every one of them down, erasing their minds, before they had a chance to kill her. She eventually destroyed the entire Society one at a time and can thus be inferred to be the best assassin left in the world. She was soon captured by Batman.
Later on her backstory would be expanded in the ongoing Batman Beyond comic series to be much more detailed:
Curare was originally a monk in the Himalayas. As a child, she bore witness to the coming of the eventual Green Lantern: Kai-Ro. Kai-Ro was discovered by a monk and brought to the ashram. Curare and Kai-Ro grew up together as surrogate siblings unfortunately, their views on life differed. Kai-Ro was happy with his life at the ashram but Curare viewed the temple as a cage and the monk elders as her keepers. Curare believed there was a life beyond the ashram that offered riches and recognition. Kai-Ro only wanted to practice humility and was content with the life he had at the temple.
The time had come to choose the next Dalai Lama. Buddhists from three other monasteries and secular clergies attended this momentous event. It was originally a tradition to have one of the elders choose a name from a golden urn left by Buddha and that name chosen would become the next Dalai Lama. However, the monks decided to go with a different tradition. A table of items was placed in front of Kai-Ro. One item belonged to the original Dalai Lama while the rest of the items did not. It was up to Kai-Ro to choose the right item. If he chooses correctly then Kai-Ro will be deemed the reincarnated soul of the former Dalai Lama.
Among the items was a Green Lantern ring (unknown to whom it belonged to originally) and the ring immediately activated as Kai-Ro moved his hand closer to the table. Kai-Ro was chosen to become the new Green Lantern of Sector 2814. The monks were astonished as well as frightened by the great power that Kai-Ro now wielded. Curare takes advantage of the moment by proclaiming that Kai-Ro has failed the test and now the monks must choose the Dalai Lama successor by picking a name from the golden urn. For some odd reason, the ring sensed deceit in Curare's soul and destroyed the urn to expose her true nature. When the urn shattered, it became apparent to the monks that the original sticks that bared different names were all replaced by sticks with only Curare's name etched on them.
The monks decided to banish both Kai-Ro and Curare from the ashram. The monks were disappointed with Curare's act of deception with the urn but more so by her refusal to accept the teachings of Buddha. As for Kai-Ro, he was excommunicated because he now holds a great power that could tempt him to abuse it. Curare believed it was Kai-Ro who actually made her plan fall apart and not the ring. Kai-Ro expresses his pity that Curare can't see past her own blind ambitions and hatred. Curare swears to Kai-Ro that the next time they meet, it will be not as siblings but as enemies.
Later on, Curaré undergoes a process performed by a dark monastery which causes her skin to develop a blue pigmentation. It is believed that this process caused some kind of facial disfigurement because Curare decides to conceal her face after suffering the transformation. Curare goes on to became the greatest assassin within the League.
Background Information Edit
Curare (spelled without the accent) is also the name of a poisonous plant used by some South American native peoples to tip their arrows, and by medical doctors as a muscle relaxant. Curare is also a Latin word, meaning "to take care of" or "to handle." This could be a subtle reference to her career, as, being an assassin, it is her job to "take care" of her victims.
Curaré has no speaking lines, other than a few grunts.
The only person to see her face is Terry McGinnis when he fought her as Batman. And judging by his reaction it is assumed that it is disfigured in some way. Due to possibly an unintentional animation error, however, her face is revealed during their first fight. Her entire head appears to be a blue skull lacking hair and a nose.