How can you master an item more than once?

One of the achievements, "Keeps on giving", is awarded if you "master any inventory item twice." But how is this possible? If, once you master an item, it stops attaining more experience points, how can you master an item more than once? What am I missing?

To master an item more than twice, you must have the version 1.2 or higher to fight the deathless kings down in the well. When you put the Infinity Blade in, the 3 doors will open and you are able to fight the deathless kings. After you defeat them, you have the privilege to go inside the big door. You fight a robot enemy named Zero Mech. Once he is killed you fight another enemy which is your original ancestor in the beginning. Once you kill him, you can start New Game+. You can re-master any item!

If you start a New Game+, any weapon that you had mastered previously you can master again. I think there is an option in the menu to start a New Game+, but there is definitely the option once you defeat the new end boss.

What you need to do is:

After you get the infinity blade, go downstairs and there will be a slot there that the infinity blade can go in to. When you insert it in, three doors will open; after you kill all three enemies, a big door will open. Go inside and kill the boss; after you kill him, you will get an option of a second mastery. Click Yes and you will see a x2 on any item at the bottom, which means second, and then you keep on going, and you get new items as well.