Building a dynamic menu based on taxonomy terms
You are looking for Taxonomy Menu module. Here is an excerpt from its project page:

Transforms your taxonomy vocabularies into menus with ease!
Features

Custom Menu per vocabulary
Uses the default taxonomy term path or custom paths
Integrate with Views
Integrate with Pathauto: use URL/path aliases
Does not interfere with other menu modules


I found these tutorials helpful to get started.
First Tutorial (youtube video).
Second Tutorial (youtube video).