Green’s Dictionary of Slang

whale v.1

also wail, wail on, wale, wale on
[? SE wale, to mark the flesh with wales (weals), or a whalebone whip]

1. [mid-19C+] (US) to hit, thrash or trounce; also fig. use.

2. to hit (rather than beat) an object.

3. [1950s+] (US black/campus) to act well, to do something especially well; thus whaling n. and adj.

4. [1950s+] (US) to attack.

5. [1950s+] to act aggressively, fast.

In phrases

whale down (v.)

[1950s+] to eat furiously.

whale on (v.) (also wail on)

to beat.

whale the — out of someone (v.)

[20C+] to beat viciously.