。
Her criteria are the top priority when choosing a marriage partner.
Literal
Her [attributive-の] conditions [subject-が] marriage-partner [object-を] choose [when/occasion-際の] priority-item is-[copula-だ].
~際 is a formal/literary noun meaning 'time, occasion,' most commonly appearing as ~の際(に) 'on the occasion of, when.' Here the genitive の is working as an attributive to modify 優先事項 ('priority item') — 'the priority at the time of choosing.' 優先事項 is a kango compound from 優先 ('priority') + 事項 ('matter, item'). The overall register is formal/advisory.