Green’s Dictionary of Slang

(US) something extraordinary, esp. extraordinarily hard to achieve.

1957		M. Shulman Rally Round the Flag, Boys! (1959) 50: We’ve had some tough town meetings before, but tonight’s going to be a bitch-kitty.
1966		‘Tom Pendleton’ Iron Orchard (1967) 397: Looks like you’ve got a real bitch-kitty here, Jim.
1978		S. King Stand 343: The sixth bolt was the one that had turned out to be the bitch-kitty.
1979		‘Iceberg Slim’ Airtight Willie and Me 9: I was having one bitch kitty of a time tuning out the interracial sewer mouth shucking and jiving.