To get the Minimalist Trophy and achievement in game, that gives you 7000 points for the shop, you need to do a complete walkthrough without opening the Item Box, not even once.

I suggest to do this on Assisted mode to make your life easier but once you've cleared the game once and you know where to go it should be pretty easy.

As you can see from my video below I didn't use any "cheat" from the shop from this run, since assisted mode already gives you 4 slots more in your inventory (2 occupied from the Assault Rifle), it's more than enough to go through this run.

For a complete walkthrough check the video below: