like a shot is an adverb meaning "without delay or hesitation; with no time intervening". It carries one recorded sense.
without delay or hesitation; with no time intervening
“he answered immediately”
“found an answer straightaway”
“an official accused of dishonesty should be suspended forthwith”
“Come here now!”
Definitions, synonyms and semantic relations for like a shot come from Princeton University’s WordNet. Commonness is measured against a corpus of everyday English. Full sources and licences.