Who's This? The 80s fashion nightmare from Who's Who Update '87 #4, page 5, by popular demand.
How you could have heard of her: In 1995, she appeared in a crowd scene in Underworld Unleashed #1, which suggested Neron would have powered her up. But none of her appearances after that corroborate this idea. Appearing as a non-costumed inmate in Arkham Asylum: Living Hell in 2003 is probably a career high, as she's mostly appeared in cameos (JSA #28, 2001; around the Intergang table in 52 #25, 2006), or as a dead body (she is found dead in Batman #651/Detective #818; then as one of the Black Lanterns in Blackest Night). In the New 52, she's appeared in a couple issues of Batman Eternal (out of costume, as an Arkham inmate), and has appeared in a number of episodes of the Beware the Batman animated series, where she is Margaret Sorrow who has poisonous claws and an inability to feel pain.
Example story: Batman #401 (1986) "A Bird in the Hand..." by Barbara J. Randall and Trevor Von Eeden
Regardless of the timeline, Magpie strikes again, stealing a priceless jewel called the Eagle's Heart right off its wearer's throat. So to speak.
Who's Next? We're going so far back, it won't even be DC Comics anymore...