My mother has borne her grief admirably.

Literal

Mother [topic-は] admirably sadness [to-に] endured-[coming-てきた]

立派に = admirably (adverb from 立派). 悲しみに耐える = 'to endure sadness' — に marks what is endured. ~てきた = 'has been doing (up to now)' — the auxiliary ~てくる in past tense marks a process that started in the past and continues to the present.