。
When she grew up, she became a famous doctor.
Literal
She [topic-は] adult [to-に] when-became famous doctor [to-に] became.
~たら is the past-conditional/temporal connector — here in its 'when X happened, Y happened' sense (a real, completed-event reading rather than the hypothetical 'if'). The structure 大人になったら有名な医者になった ('upon becoming an adult, became a famous doctor') is a bit unusual — for a stable past biographical fact, 大人になって ('becoming an adult, then...') would be more natural. The ~たら version suggests the second event was somewhat unexpected or noteworthy at the moment of realization.