A full-stack web developer is a technology expert who can work on both in the front end as well the back-end of any application. The person should be familiar with each layer of a 3-tier model.
You need to know the following to become a full stack developer
Backend- Ruby on Rails, PHP, Angular2, Node.js
Database- MySQL, MongoDB, CouchDB
Debugging- Grunt, Xdebug
Version Control- GIT, Subversion