She endured her grief without shedding a single tear.
Literal
She [topic-は] tear one not-spilling sadness [to-に] endured.
涙ひとつこぼさずに ('without spilling even one tear') uses the ~ずに pattern — the classical negative functioning as 'without doing.' ひとつ ('one') adds emphasis on the total absence. 悲しみに耐えた means 'endured sadness.'