You can increase your inventory by picking up the backpack upgrade. The first backpack will be in the safe room in the Old House. The Old House is the same area where the "Mia" video tape takes place.
Go on to the balcony from the projector room (where you hid from Marguerite in the tape) but turn left this time. Down the wooden walkway will be the safe room, and the backpack will be sitting on the table. Interact with it to automatically increase your item slots and unlock the achievement.
There are other backpack upgrades later on in the story, but this is the soonest you can unlock this achievement, and also a very easy one to find. Your second upgrade is found in the room attached to the Master Bedroom in the Main House. The last backpack upgrade is in the Ship.