In order to master a weapon style you have to use your ability points to completely max out an ability tree. For example, if you are a warrior one of the tree's you will have is called two-handed.
Spend your points on each of the abilities in that tree, and the corresponding upgrades to the abilities until every part of that combat tree is lit up indicating you have bought it. Upon confirming your skill selections the achievement will pop up.
NOTE: You can do this by upgrading a companions ability tree all the way (example: Avalenie's Weapon and Shield Tree) but you CANNOT get this achievement by upgrading a mage's spell tree fully (example Bethany's Elemental tree)