Implementing Taxonomy hierarchy in View and Search
I would look into using Search API for this and build up facets using the Facets API.

Once you have Search API installed you need to create a search index, choose which fields to index and what facets to create.

With the search index in place you can from Views create a Search view that uses your index as base. 

Place the facets where you want them and tell them to show up at your search views url.

There is a guide that explains how to setup Search API here. In the guide they use Apache Solr as backend for the search index. That is not necessary, you can use the database as backend but I recommend using Apache Solr as backend as I've stumbled on a few bugs in the database backend which work with Solr.

You would be able to do searches such as this:



Good luck