。
She would never change her convictions.
Literal
She [topic-は] self [possessive-の] convictions [object-を] never change-try-to did-not.
自己 (じこ) is a Sino-Japanese reflexive ('self') that's far more abstract and formal than the everyday 自分 — common in compounds like 自己紹介 ('self-introduction'), 自己満足 ('self-satisfaction'), 自己責任 ('personal responsibility'). 信念 ('belief, conviction, faith') carries weight — not casual opinion but firmly-held principle. 決して...ない is a fixed adverbial frame requiring negation: 'never, by no means, in no way.' 変えようとしなかった = 'didn't even try to change' — the past negative of ~ようとする. The combination paints unyielding resolve.