This achievement is one of the more annoying ones to earn, albeit easy to achieve.
You CAN use the two extra hip pouches earned through the shop.
You CAN reload a save if you make a mistake.
To do this I recommend playing on STANDARD and NOT Assisted. The reason for this is in Assisted mode Jill starts with an Assault Rifle which takes up two inventory slots. Obviously you cant put this in the item box due to the nature of the achievement.
(NOTE: Cryptic Flair pointed out that by starting out on Standard mode and letting zombies kill you a few times after collecting your bonus hip pouches, the game will ask you if you wish to switch to Assisted. Doing this will allow you to play on assisted mode with your additional extra pouches and the Assault Rifle.)
Play through the game on your preferred difficulty, being careful not to interact with the item box. Keep an eye out for handgun ammo and do your best to always keep at least one extra heal on you. I recommend never having more the two full stacks of one item as it will take up precious inventory space.
Picking up the grenade launcher will take two inventory slots along with the additional ammo taking up more. I chose to pick up the grenade launcher and had about one or two free slots left which is enough to get you through the game.
If you don't want to pick up the grenade launcher, I definitely recommend at least grabbing the shotgun. Otherwise you'd be doing a "pistols only" run with Jill. Props to you if you do that.
Its VERY important to make use of the Hip Pouches found throughout Racoon City. Here is Gamespots guide to find all 6 of them- https://www.gamespot.com/amp-articles/resident-evil-3-remake...
Aside from that, this achievement is fairly straightforward. Here are some extra tips I utilized.
-it's very easy to open the item box by mistake. To avoid this make sure whatever your trying to interact with has the button prompt to interact with it before doing so. If you think you made a mistake, check your records tab. Under the challenge called "Minimalist" it will show how many times you opened the box. If it's more then zero, you will need to reload your save.
-Make sure your always combining items together to increase space.
-You can still combine items from the ground even if you dont have space to pick them up.
-If you have a small stack of a minor item (ie. handgun ammo, red herb, etc) dont hesitate to drop it. Those item are in abundance unless you're on a higher difficulty.
-Dont worry about picking up many flame rounds. Flame rounds aren't the most effective thing against bosses. Although they are nice to use as an alternative to your precious explosive rounds, the game gives you a lot of flame rounds. It's okay to keep a full stack but I would throw away the rest.
-Dont worry about Explosive B. As the tip above describes, flame rounds aren't too important. Acid rounds are provided toward the endgame segment just before fighting 3 Hunter b's. Because of the power of explosive rounds, try to only collect and craft them by combining two Explosive A.
Any further information you guys provide or I discover I will update this solution with. Please leave your feedback and good luck gamers!