。
She traveled all over the world.
Literal
She [topic-は] earth [possessive-の] here-and-there [object-を] traveled.
地球のあちこち ('here and there around the globe') uses あちこち ('here and there / all over'), a reduplicated word expressing scattered locations. 地球 ('Earth/globe') rather than 世界 ('world') gives a more physical, geographical feel. を marks the space traversed by the travel.