。
She finally made up her mind to go abroad.
Literal
She [topic-は] finally foreign-country [to-に] go decision [object-を] did.
決心をする ('make a decision, resolve') uses 決心 ('determination, resolve') with the light verb する; the alternative 決心する (suru-verb form) is also common, with the noun-version slightly heavier in feel. The relative clause 外国に行く ('go abroad') modifies 決心 as the content of the decision — a direct attachment without のする intermediary. ついに reinforces the long-built-up arc: this is a decision the speaker has been weighing, not a snap choice.