。
Our party will oppose this to the bitter end.
Literal
Our party [topic-は] this [dat-に] to-the-end oppose-[polite-ます]
わが is a slightly formal/literary possessive meaning 'our/my' — わが党, わが国, わが社 are common collocations in political and institutional speech. 飽くまで (あくまで) is an adverb meaning 'to the end, persistently, stubbornly' — here, committing to oppose without compromise. The stiff register (polite ます, literary わが) fits a political statement.