When hair is the main problem, liquids often won't cut it. You need a tool to physically pull the clog out. A "Zip-It" tool is a cheap plastic strip with barbs found at most hardware stores. Alternatively, a wire coat hanger works in a pinch.
If you prefer to avoid harsh chemicals, several effective home remedies can clear minor to moderate clogs. What to Do When Your Bathtub Is Clogged - blocked drain? bath drain unblocker