What is the meaning of 赶上 in ...完全是赶上了好时代?
"In time for" is the right interpretation in this context. 好时代(an era when living was great) is like a party. It has a beginning and an end. People who died before it or born after it missed out. "她赶上了好时代" means she was born at the right time, during a great era. 

赶上 means " (rushed in or hurriedly arrive) just in time."