at once vs like a shot

at once and like a shot both are adverbs.

Word	Noun	Adjective	Verb	Adverb
at once	No	No	No	Yes
like a shot	No	No	No	Yes

As adverbs, at once and like a shot are synonyms defined as:

at once and like a shot: without delay or hesitation; with no time intervening

Other synonyms of at once include directly, forthwith, immediately, instantly, now, right away, straight off, straightaway.

at once (adverb)	like a shot (adverb)
without delay or hesitation; with no time intervening	without delay or hesitation; with no time intervening
simultaneously