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She made a major discovery while still a young research student.
Literal
[topic-は] still young research-student [during-the-state-of-うちに] big-discovery [object-を] made.
うちに ('while [in a state], during the period of') marks a window of time defined by some condition — 若いうちに ('while young'), 元気なうちに ('while still healthy'), 学生のうちに ('while a student'). The implication is often 'before that condition changes' — there's a sense that the window is finite. 大発見をする ('make a big discovery') uses 大 ('big, great') as an intensifying prefix on 発見 ('discovery'). 研究生 ('research student') is a specific status in Japanese universities — students conducting research without yet being formally enrolled in a degree program, or in transition between programs. Together the sentence celebrates an early-career achievement.