Como Barbara Gordon (Oracle) ficou incapacitada?

De Wikia :

As the years went on, however, Barbara found her role as Batgirl less and less fulfilling, and she eventually more or less retired.

That's when the Joker showed up at her house, shooting and paralyzing her and when he kidnapped her [father]¹. Batman rescued Jim Gordon, but 19-year-old Barbara Gordon's career as a crime fighter was over. She spent a month in a deep depression.

Isso aconteceu em 1988 "Batman: A Piada da Morte "

Além disso, mais detalhes estão disponíveis em Wikipedia :

Following the editorial retirement of her Batgirl persona in Barbara Kesel's Batgirl Special #1, Alan Moore's graphic novel Batman: The Killing Joke depicts the Joker shooting her through the spinal cord in her civilian identity, resulting in paraplegia.

In subsequent stories, editor Kim Yale and writer John Ostrander establish the character as a computer expert and information broker known as Oracle.

¹ A Wikia identifica incorretamente Jim Gordon como o tio de Bárbara.

Como resposta à pergunta colocada no título:

The character made her first comic book appearance as Oracle in Suicide Squad #23, anonymously offering her services to the government's Task Force X. In the following two years, Oracle … made guest appearances in various DC titles until her identity was revealed to be Barbara Gordon in Suicide Squad #38 (1990). She officially becomes a member of the Squad in issue #48, following an invitation from Amanda Waller.