She did nothing but grieve over her husband's death.

Literal

She [topic-は] husband's death [object-を] grieving [nothing but-ばかり] was.

嘆き悲しむ is a compound verb — 嘆く (lament) + 悲しむ (grieve). ~ばかりであった means 'did nothing but,' with the formal であった ending.