Blade Kitten

Starting with level 2 you can access the shop by hitting Back and choosing Weaponarium. There are 3 swords for you to by here, scroll right past the food until you find them.

Total cost for all 3 is 275,000 hexes, so just save up until you can buy them all. Simply playing through the game and going for all the items will get you enough hex to buy all the items.

EDIT: 01/17/13--Made a few corrections and changed the primary method to the superior one pointed out by MysticWeirdo.

Depending on whether or not you buy HP and/or Stamina upgrades, costumes, and the order in which you do so, you may need many more hex to afford all the Free Blades. Since the costumes don't improve the character's stats I would recommend buying the Free Blades and HP and Stamina upgrades first as you play through the game, then use the following method to get the last few costumes after finishing the final level.

In any case, here is what is probably the fastest way to earn hex in this game (with gratitude and credit again going to MysticWeirdo):

First, you'll need to have played through the game until you've reached level 9 which is called Berserk. Load that level. Press "B" to skip the opening cutscene. Double-jump up and to the right to land on the edge of a floating vehicle. Then double-jump to the left to land on another one. Now jump to the left and run left along an awning to collect five green hex, then jump left onto a ledge and collect the fish-in-a-bag worth 10,000 hex.

Now press the "Back" button to bring up the menu with the Level Select option. Scroll up once to go to the bottom of the list and press "A" on Level Select. This will bring up the list of levels and Berserk should already be selected so press "A" again. The game will warn you that "Changing levels will reset current level checkpoints." but you keep your accumulated hex so just press "A" again to reload the level. Then just repeat the process until you have enough to buy everything in the game you don't yet have.

Now here is the alternate method that I originally had posted. MysticWeirdo's method is better because it's faster, more lucrative, and has one less cutscene and no enemies. Whereas the following method is only advantageous due to being available one level sooner (and thus could perhaps be used to acquire some upgrades earlier during your initial playthrough if you wanted) and provides an optional change of scenery in case for some reason you get tired of the other way after a while. Anyway the other method is as follows...

Load level 8 which is called Darque Nights. Press "B" to skip the opening cutscene. Go to the right and after a couple seconds you'll trigger another cutscene so press "B" to skip that one too. Continue to the right (pressing "X" to defeat the Darques along the way) following the trail of 9 yellow hex down a small flight of stone stairs then soon up another stone staircase. When you reach the flat part at the top of the stairs look up and you'll see a wooden beam connected to an awning that you can either double-jump up onto or jump and hang from the bottom of and crawl left and up on (if you can't quite see it try moving the right analog stick diagonally up and to the right). Go ahead and jump up there and run right and up the awning to get a fish-in-a-bag. Then, as with the 1st method, just keep reloading the level until you've accumulated as much as you want.

Once you get the hang of the 1st method you should be able to earn 10,000 hex about every 20 seconds or so. I would recommend making this one of the last achievements you get in this game as you will obviously be accumulating many thousands of hex throughout the subsequent levels if you have not yet played them. I hope this helps and if you have any corrections or tips to make this solution better please leave them in the comments. Thank you!