。
She was raised well by her parents.
Literal
She [topic-は] parents [by-によって] splendidly was-raised.
によって marks the agent in a passive construction — 'by her parents.' 立派に (りっぱに, 'splendidly') is the adverbial form of 立派. 育てられた is the passive of 育てる. The によって agent-marking is more formal than に alone.