For and by are called prepositions. Prepositions must always me followed by a noun or a pronoun and that noun or pronoun is called the object of preposition. *** BY Used to indicate proximity: Can I sit by you? He was standing by me. The post office is by the bank. Used to indicate the person that does something in a passive voice sentence: The microwave was fixed by the mechanic. The flowers were delivered by a postman. The branch office was closed by the head office. Used to indicate an action with a particular purpose: You can pass the exam by preparing for it. I expressed my feeling toward her by writing a letter. She finally broke the record by pure effort. Used to indicate a mean or method: Please send this package to Russia by airmail. I came here by subway. *** FOR Used to indicate the use of something: This place is for exhibitions and shows. I baked a cake for your birthday. I put a note on the door for privacy. She has been studying hard for the final exam. Used to mean because of: I am so happy for you. We feel deeply sorry for your loss. For this reason, I’ve decided to quit this job. Used to indicate time or duration: He’s been famous for many decades. I attended the university for one year only. This is all I have for today.

In your particular questions, you cannot say "..have often been overshadowed FOR her personal life" because "for" does not describe WHAT is doing the overshadowing. For example, it the complete sentence is "Her work has often been overshadowed by her personal life." You can remove "by her personal life" and it is still a sentence; this short addition to the sentence is describing what is overshadowing her work, which is her personal life. I hope this makes sense! If you are familiar with linguistics, then look at it like a syntax tree.

English verbs meaning change with the addition of various prepositions. I can go for a ride. I can go by bus. I can go to a store. I ran from trouble. I ran into a neighbor means I encountered her. I ran into a neighbor's yard mean I entered her property. Often you need to learn the prepositions case by case.