at once vs at one time

at once and at one time both are adverbs.

Word	Noun	Adjective	Verb	Adverb
at once	No	No	No	Yes
at one time	No	No	No	Yes

As adverbs, at once and at one time are synonyms defined as:

Other synonyms of at once include at a time.

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