This walkthrough won't give directions in the way of going north or west twice. It just lists what to do in certain locations. Similar to the hint section, clicking on the part where you're stuck displays the list of actions needed to continue as well as the points you can earn there.

Finding the Mirror

Clearing with rock

  Move the rock west of the castle (2)
  Get the dagger from the hole under the rock (5)

Oak tree

  Climb the oak tree (2)
  Get the golden egg from the nest in the oak tree (6)

Lake west of rock screen

  Get a handful of pebbles from the bank of the lake west of the rock & dagger screen (1)

Lake north of carrot garden

  Talk to the elf near the lake and get the magical ring (3)

Old well

  Take the bucket either by cutting the rope above the ground, or taking it while it floats in the water (2)
  Enter the well either by sitting in the bucket or climbing the rope after lowering it (2)
  Fill the bucket with water (2)
  Dive to the bottom of the well (4)
  Enter the lair of the dragon (1)
  Throw water at the dragon (5)
  Get the magic mirror (8)
  Leave the lair of the dragon through the western exit (2)

Finding the Chest

Gingerbread house

  Eat a piece of the gingerbread house (2)
  Open the cupboard in the gingerbread house (2)
  Get the piece of cheese from the cupboard (2)
  Get the note from the nightstand of the witch (1)
  Read the note (2)
  Push the witch into her own cauldron (7)

Carrot garden

  Get a carrot (2)

Goat pen

  Show the carrot to the goat (5)

Troll bridge

  Have the goat bump the troll off the bridge (4)

Gnome's dwelling

  Get the beans after guessing the gnome's name (9)

Fertile soil

  Plant the beans (2)

Cloudland

  Reach the top of the beanstalk (2)
  Get the slingshot from the hole in the tree in Cloudland (2)
  Tire out the giant (7)
  Get the magical chest (8)

Finding the Shield

Stump and log near lake

  Look inside the stump (1)
  Take the pouch from the stump (3)
  Open the pouch (3)

Walnut tree

  Get a walnut from the nuts at the foot of the walnut tree (3)
  Open the walnut (3)

Clearing north of elf lake

  Get the magical bowl (3)
  Look at the bowl (can also be done before picking it up) (1)
  Say the magic word and fill the bowl (by using it on yourself) (2)

Woodcutter's cottage

  Give the filled bowl to the woodcutter (3)
  Take the fiddle (3)

Clover patch

  Get the four-leaf clover (2)

Entrance to dragon's cave

  Jump and grab the condor's talons (3)

Meadow west of the hole

  Get the mushroom (1)

Down the hole

  Give the piece of cheese to the giant rat (2)

Leprechaun's antechamber

  Play the fiddle for the leprechauns (3)

Throne room

  Take the magic shield (8)
  Take the scepter from the throne of the leprechaun king (6)

Chamber with small hole in the wall

  Eat the mushroom (and then quickly walk through the hole) (3)

Front gate of Castle Daventry

  Open the front gate of the castle and enter (3)

The End!

Alternate Solutions

  Kill the dragon by throwing your dagger at him (3)
  Get a key after failing to guess the gnome's name (3)
  Unlock the door in the mountain with the key (2)
  Kill the giant by shooting a pebble at him with your slingshot (3)

Actions that will actually make you lose points

  Drink water from the bucket (-2)
  Eat the carrot (-2)
  Allow goat to walk away by going back into the pen (-5)
  Eat stew from the magic bowl (-2)
  Give the golden egg away to the troll/rat/woodcutter (-6)
  Give pouch to woodcutter/rat (-3)
  Give opened pouch to troll (-6)
  Give closed pouch to troll (-3)
  Give walnut to troll/rat (-3)
  Give walnut to woodcutter (-6)
  Give the carrot to the woodcutter (-2)
  Give the mirror away to the troll/rat (-8)
  Eat the magic beans (-4)
  Throw your dagger away (-5)
  Give the ring away to the troll/rat (-3)
  Give the chest away to the troll/rat (-8)
  Give the scepter away to the troll/woodcutter (-6)
  Give the shield away to the troll (-8)