Green’s Dictionary of Slang

bitters n.

SE in slang uses

In phrases

get one’s bitters (v.) [SE bitter end]

(US) to get one’s deserts.

1825		J.K. Paulding John Bull in America 204: But to use the landlord’s choice phrase, ‘he got his bitters’ – that is to say, he was shot through the head by mine host.
1844		St Landry Whig (Opelousas, LA) 5 Sept. 1/5: The seal soon got his bitters, and the captain cut a big hunk off the tail end.