、。
She insisted that I complete this work by tomorrow.
Literal
She [topic-は] me [to-に], tomorrow [by-までに] this work [object-を] complete [as-ように] [quotative-と] said-and-wouldn't-listen.
Two grammatical structures combine for an emphatic insistence. (1) The deadline marker ~までに ('by [a time]') sets a hard time-limit — distinct from the more durational ~まで ('until'). (2) The fixed expression 言って聞かない (here 言ってきかなかった in past) — literally 'said and wouldn't listen' — is the standard idiom for 'kept insisting, wouldn't take no for an answer.' The 聞く ('listen') here is in its 'listen to' sense: the speaker said her piece and then refused to hear any rebuttal. 完了する ('complete, finish') is a Sino-Japanese verb common in formal/business contexts.