Green’s Dictionary of Slang

boost v.3

[? bust v.1 (5b), i.e. to hit]

(US) to attack.

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[US]J. Dixon Free To Love 95: ‘Boost!’ Fritz was standing in the path, a heavy stick in his hand. [...] ‘That’s no good,’ he grumbled. ‘He come back here boddering you and I boost’ [...] ‘He wants trouble? Then he gets it. I brain him mit the stick!’.