This is a short guide I've written up for anyone having trouble with understanding what the items in the Greedy Challenge do (and my thoughts on each of them). I probably got a couple things wrong, so if you know of anything that's missing or incorrect, feel free to comment!

"An option that can attack appears"

Appears and shoots at the enemy after you hit them, then disappears for awhile. Does 4 damage per shot and can't break barriers.

Pretty decent for DPS.

"Reusing spells becomes faster"

Increases water gain. Upgrading it makes the effect even stronger.

Really good, in my opinion!

"Attacks your surroundings when you graze on the ground"

Dashing on the ground creates a small gust of wind that deals 12 damage. It can break barriers.

Sounds good on paper, but I haven't really gotten much use out of it.

"An anchor falls when a 10 hit combo is reached"

An anchor falls onto your opponent for 18 damage when you reach a 10 hit combo. Unfortunately this doesn't trigger again when reaching 20, 30, etc. Breaks barriers. Upgrading it increases the damage dealt.

Overall an okay item but it seems to just miss a lot of the time.

"While the enemy is in a Spell Break, your attack power increases"

All damage dealt is increased while the enemy is staggered. Upgrading it increases the damage dealt even more.

Extremely powerful. Probably the best item in the game?

"Searches the boss if you attack while their magic circle is red"

Breaking a barrier sends out 3 homing spikes that deal 8 damage each.

One of the strongest DPS items. Annoyingly can knock the boss away from you during a spell break, but still overall a great item.

"When grazing bullets and attacking at the same time, it will attack around you"

I have absolutely no idea what this does. I cannot seem to get it to activate no matter what I try.

Probably not worth taking(?)

"Attacks when you collect water"

Collecting water will shoot out bouncing bubbles that do 4 damage each. Can't break barriers. Upgrading it increases its damage.

Overall, a pretty decent item that synergizes really well with characters that collect water a lot such as Reimu.

"It can enlarge your graze area once while in the air"

You gain the ability to airdash off of a web when you would typically be out of them. (still doesn't work without stamina)

Probably great for Murasa and maybe Yuuma?

"Shoots after using a Spell Card"

Using a spell card also now fires 3 slow moving shots forward for 12 damage each.

Good luck getting more than one of these to hit. Probably one of the worst items.

"Attacks your surroundings when you graze just in time"

Grazing danmaku will send out 4 music notes in a square formation that do 12 damage each. Operates on a cooldown. Can't break barriers.

It's okay, don't expect this item to help you out too much, most of the music notes just end up missing...

One important mechanic not mentioned in-game is the Challenge Level.
For every time you enter the Land of the Backdoor and for every item you collect, the challenge level will increase by one, giving the bosses more HP and changing the order of some fights. If the player reaches challenge level 20 after fighting Okuu, ALL damage taken will equal a full life orb.

Also, Yuugi does actually have an item, but it seems to have been removed in a recent update.

And for how healing works: Playing on Easy will reward you with a full heart at the end of each boss fight. Playing on Normal will only reward you with half of one, and playing on Hard rewards you with NOTHING. (What the flip Twilight Frontier???)

This is my favorite spinoff in the entire franchise, and its a shame this mode never got fully translated. I hope this guide can provide some assistance to anyone having trouble!