like a shot vs at once

like a shot and at once both are adverbs.

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

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

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

Other synonyms of like a shot include directly, forthwith, immediately, instantly, now, right away, straight off, straightaway.

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