Parchments are a bonus thrown into the game that (slightly) changes the ending if you collect them all. You get pieces of parchment for collecting all the items in a stage (except for those dropped by fallen enemies).
Below is a list of what you must collect in each chapter to receive that chapter's parchment.
Once you have a sword, go to where you started the stage. Go to the upper tight of that area and slice the trees until you find one that disappears, leaving behind a heart refill. Go to the bottom left of this area and go clockwise along the wall slashing at the edge and the area to the right will change, revealing a large gem.
Inside the castle, find the dog by wandering around, find and talk to all the people to return the dog. (You must speak to the dog's owner twice) He'll give you the shield. Explore the castle for a large gem. Once you open the secret passage and the ghost door you will find a heart container, grappling hook and compass.
In the dungeon you can find a heart refill.
Buy a shovel from the man selling it. In the area with the lines coming together in one spot dig for a heart container. Explore this chapter before riding through the wind on the horse to find a large gem.
In the cave you must find the stick, search all the chests.
Once you have the stick and have saves the top screen talk to the farmer and dig up his land (to the right) until you have a large turnip.
In the dragon field you can find a heart refill and a slingshot.
On the main screen there are 3 easily found eggs and a dragon scale. There's another egg on the screen to the right, and another in the cave which also holds a gem. After retrieving the eggs you must off the knights until you get a key, then bring that to the dragon.
At the bridges go up then right to the 2nd bridge. Go right from here for a heart container, then back and down the 2nd bridge. Go right from here and you can find a heart refill.
When sledding on the left will be a heart refill. Answer all of Merlin's questions correctly for a heart container. Inside the cave there is a large gem in one of the rooms.
There is a large gem laying around in plain site. Go to the stone and follow the clues with your shovel for the whistle. Use the whistle on the bird for the stone bracelet. The snorkel should be in plain site. When Merlin asks if you want to solve extra puzzles for a prize, say yes. It's a heart container, and it's in the 3rd extra puzzle room. I can't remember if this stage had a heart refill (and forgot to note it) but if it did it was in plain site. use the compass.
Go down, right and up for a heart container. Go down from Garret for a heart refill. When you reach the tooth cave area the orange is in plain site. Go left after exiting this area for an apple. Follow the side clockwise for a large gem.
Talk to the bird, then the man in the one open house for seeds. Talk to the bird and have him follow you clockwise around the castle walls. Continue this until he's ct open a way to the insect, the large gem and a key. In the stable dig in the hay for a key, and the heart container will be in plain site as you leave. Talk to the man in the right-most house for a key. Go inside and get through the key maze. A heart refill is in one of the rooms inside the boss chamber.
In one room most of the floor is gone and you have to hop along the remaining flooring to the other side. When you do keep our eyes on the right side of the screen for a large gem, the least item you have to collect. (This stage has no heart container or heart refill)