。
She accused me of not replying to her letter.
Literal
She [topic-は] letter [of-の] reply [object-を] give-not [quotative-と] me [object-を] blamed.
非難する (to blame/criticize) takes the person blamed with を. The content of the accusation — 手紙の返事をくれない (not giving a reply to the letter) — is quoted with と. くれない uses the negative of くれる (to give/do for me), so the complaint is specifically that the reply wasn't given for her benefit. The nested structure (quoted complaint + accusation verb) is a natural pattern in Japanese for reporting what someone blamed you for.