A very easy way to dissolve hair in a drain whether it be a sink drain, shower drain bathtub drain etc is to pour a cup of liquid bleach down the drain that has the hair in it.
Liquid bleach will break down and dissolve the hair since the hair is acidic.
If you don't have any liquid bleach around the house you can use Baking Soda and Vinegar to dissolve the hair in the drain as well.
Pour 1/2 cup of baking soda down the drain and then after putting the baking soda in the drain pour a cup of vinegar down the drain and then let it fizz.
When it's fizzing it will break down and dissolve the hair in the drain.
Be sure to plug the drain up with a drain stopper and some tape such as duct tape or place something over the drain cap to prevent the baking soda and vinegar from coming out the drain.
Let the Vinegar and baking soda work it's job in the drain for at least 30 minutes and then remove the drain stopper and pour some boiling water down the drain and the hair should be gone.