She advocated for the elimination of discrimination against women.
Literal
She [topic-は] women-discrimination-abolition [object-を] advocated.
女性差別撤廃 is a four-kanji compound: 女性 (women) + 差別 (discrimination) + 撤廃 (abolition/elimination). This kind of stacked noun compound is common in formal Japanese — each pair of kanji adds a layer of meaning. 主張する means to assert, argue, or advocate — it carries the weight of a principled public stance, not just a casual opinion.