Strictly speaking, you don't need a mentor to get good at anything. However, it can really help in the areas that are defined more by people than by things working or not.

As a mentor, I have found that is mostly about reviewing others work and thinking and giving feedback. For instance, you don't really need a mentor to get better at solving problems. You may need a mentor to help you communicate details about the solution.

Somewhat related: http://jeffrey.io/writings/apprentice.html