What is a delicate way of identifying key insiders? I am beginning a doctoral program this Fall and have been receiving helpful advice from a recent graduate. While this graduate has mentioned a key mentor that will likely serve as my primary advisor, I am curious to know if there were other mentors instrumental to his success in the program.

What might be a delicate way of inquiring who these people are?

EDIT: I was initially afraid that having someone identify the "good guys" might imply that I reckon that some are "bad." But this is probably overthinking it, as one comment pointed out.
Let me just emphasize one thing: there are very few objectively good advisors/mentors. It really depends on both the mentor and the student’s personality. Some prefer a more hands on approach while others like to be independent. Some are motivated by harsh criticism while others need a more gentle approach. 

To conclude, I think what you’d want to ask is more “what is Professor A like?” rather than whether they’re good/bad mentors.