This guide will only cover rare/unique items. For regular items that you find more than once, the guide will be limited to invisible/hidden chests. By "hidden" it implies that it is partially or entirely being covered by a foreground element
This guide won't include easily found items that only require minimal deviation from the regular stage route!!
This guide will cover specifically item locations on hard mode!! (Though most of them, if not all, will be the same for normal and hard mode)

It's very possible that this guide won't cover every single instance of hidden chest, but it will be updated accordingly as more hidden chests are uncovered.

Be aware that an item only gets available on the shop once you finish a stage carrying that item. That means that if you drop it without noticing or consume it entirely in the same stage you picked it up, it won't appear on the shop later!

Hidden chest behind the AA gun with a minigun.

You will need to have a hovering platform to access this item (item acquired on stage 4). Upon flying all the way over this beginning area, you will find a hidden chest with a money cat. Necessary for serious scoring runs.

Invisible chest with a blowpipe dart. An extremely rare item, as it is great for melting boss HP.

Invisible chest in a floating platform with a milk gallon, as if the game didn't shower with enough healing items.

Hidden chest inside the air ventilation system with a golden fan. A rare item that is fundamental for scoring.

Invisible chest floating at the side of the ladder with the unique explosive jar item. It deals a massive damage in a large area, and it's great for finishing off the stage 2's boss quickly.

Invisible chest inside the top gas corridor with a rocket launcher. A pretty rare weapon that deals a lot of damage.

Invisible chest near the boomerang thrower with an apple. Quite useless unless it's your first time playing the game and you're still overdosing on healing items.

Invisible chest at the edge of the iron bar with another blowpipe dart.

Invisible chest at this corner with a full healing item of the same kind to the one more easily found in stage 1.

An invisible chest at this corner at the end of the auto-scroller with a spinner. A weapon that can be circumstancially really useful.

Hidden chest with a wave-throwing blade. Somewhat easy to miss because of how the objects you need to climb blend well with the environment.

Hidden chest with melee iron gauntlet. An obvious chest, but since it is technically "hidden", it is included in this guide.

Hidden chest in that tower with a golden fan. Necessary for scoring runs.

Two hidden chests at the floating platform above the limit of the screen with the hovering platform item and the traditional japanese meal food. The hovering platform is a unique item that will be necessary to get another unique item in stage 5, and the traditional japanese meal is one of the few full healing items available in the game.
In order to get to this platform with the chests, you need to pogo into the vertical flying drones in sequence, making you go up higher than your regular jump.

Invisible chest at the side of the ladder with a golden mallet. Good item for scoring.

Climbing the previously mentioned ladder gives you access to this area. Here you can find a chest with the unique infinite-use sword. It deals a decent damage.

At this area of stage 5, various items are hidden in these areas where you can climb to.

Invisible chest floating at the corner of the secret room with a wave-creating sword

Hidden chest in this secret room with a full healing item.

Invisible chest in this secret room with an energy orb.

Invisible chest floating up there at the beginning of the area with a full healing item.

Here you need a hovering platform to be able to reach the plaform that is off-screen (you can find the hovering platform on stage 4). Here you will find a hidden chest with the unique confeti item. It continuously deals damage to all enemy entities on the screen for an extended period of time. Can be useful for some sections.

An invisible chest in this corner with a flamethrower drone. An extremely strong and unique way of dealing damage. Might be useful for speedrunning.

A chest hidden by the foreground with a rocket launcher. A strong weapon, but probably not very useful at this point of the game.

A chest hidden in this room with a spinner. A weapon that can be circumstancially really useful.

An invisible chest at this platform with a money cat. You need to get that for scoring.