This is a pretty simple achievement to unlock as all you need to do is purchase the rune slot upgrades in the game menus.
In the game menu attribute tree, you can unlock additional rune slots for all your weapons. This achievement is only for the sword, not the bow or the dagger. You already have one slot unlocked when you start the game and the two additional rune slots will cost 60 and 180 Mirian, respectively, and therefore you will need 240 Mirian to complete this achievement.