Green’s Dictionary of Slang

(US) to attack or work at something vigorously, esp. when vocalizing a point; usu. as whale away at.

c.1850		F.M. Whitcher Widow Bedott Papers (1883) 24: You remember that one that come round a spell ago, a whalin’ away about human rights.
1856		‘Q.K. Philander Doesticks’ Plu-ri-bus-tah 126: Then, at once, squared off at Cuffee, / Instantly ‘sailed into’ Cuffee; / And he whaled away at Cuffee.
1873		‘Mark Twain’ & C. Warner Gilded Age 47: Spread her wide open! Whale it at her!
1886		Harper’s Mag. July 322/1: In tones of wrath [...] he whaled it at his opponent throughout the fifteen minutes allotted to him [DA].
1914		Bulletin (Sydney) 17 Sept. 32/1: Although warned by the referee he whaled into Holland, and, utterly reckless of where and how he hit, roughed and hustled Holland across the ring [...] – and was disqualified.
1956		Billie Holiday Lady Sings the Blues (1975) 45: When Fanny landed her first blow on Mom, I got into it and started whaling away at Fanny.
1971		R.D. Pharr S.R.O. (1998) 62: [of sexual intercourse] To lay up with a chick, whaling away while Gloria was rotting in jail.
2003		McGill Reed Dict. of N.Z. Sl. 229: whale into Attack vigorously. ANZ C20.