。
The blind nurse devoted herself entirely to caring for the elderly.
Literal
Eye [subject-が] not-seeing nurse [topic-は] elderly [possessive-の] care [object-を] do [nominalizer-こと] [to-に] whole-body [object-を] offered.
Two relative clauses stacked: 目が見えない modifies 看護婦 ('the nurse whose eyes do not see'), and 年寄りの世話をする modifies the nominalizer こと ('the act of doing the care of the elderly'). 一身を捧げる ('to offer one's whole body') is a set expression meaning 'to devote oneself completely, body and soul' — the 一身 (one-body) captures that it's the entire self being offered. The に on こと is the target marker: what the devotion is directed toward.