It’s very easy to remove taxonomy base slug from url.
Suppose your old url like this : http://mysite.com/project-category/category1
and your new url like this : http://mysite.com/category1
You have couple of plugins for this.Some of are as under
1) Remove taxonomy base slug
remove-taxonomy-base-slug.
2) Seo ultimate
Seo ultimate
Install and configure plugin as per give instruction in plugin.
Enjoy It.