。
I have no obligation to explain my big screw-up to you.
Literal
I [of-の] major blunder [about-について] you [to-に] justify obligation [topic-は] not-exist.
について is the compound particle for 'about, regarding, concerning.' 弁明 ('justification, explanation, excuse') is a formal legal-sounding noun. The pattern 義務はない ('have no obligation') is the standard denial of duty. An assertive, slightly combative statement — the speaker is refusing to account for themselves.