The Mountain Maze is a lengthy and oftentimes confusing area.  There aren't many points of interest, so keep track of Willow's travels as much as possible. An important thing to note here is that Po's Ocarina does not work in the Mountain Maze, so be prepared to watch your health and do a lot of running. This place can be the first real challenge you've experienced in Willow's quest - particularly if you're playing legit and not regularly saving/restoring from an emulator. I still have fond recollections of wanting to break my NES controller when I was ten years old before having the sense to make a map. Refer to the included Area Five Map to help you survive.

The first point of interest will be the Monster's Bone, better known as the Magic of Specter. From the entrance to the Mountain Maze, keep east as much as possible, heading north when Willow can, to a chest at the dead-end. It is necessary to obtain this item before advancing the plot, so be sure to do this first.

A ways southeast of the treasure chest, Willow will find a small home.  Herein is an old lady who claims to know nothing of Nockmaar Castle (I call her Thunder Lady), but will restore Willow's health and magic at any time.  Additionally, she teaches the adventurer the Magic word of Thunder.

Immediately after exiting the Thunder Lady's home, head one screen north.  Here Willow will find a treasure chest blocking a path to a cave.  The stairs heading up the mountain actually lead to Nockmaar Castle, but Willow will need to find another way to access it.  The treasure box contains a Healball, which functions in a similar fashion to the Healmace (only stronger).

Northeast from the Thunder Lady's home look for another chest.  This contains the Tail Shield, a powerful shield fashioned from the tail of a demon.

After wandering the Mountain Maze for a long enough time, Willow will find evidence of some water and some green grass veering off to the west.  Here the ground is covered with little mouths that will damage Willow if he tries to cross over on foot.  Use the Magic of Specter to transform into a monster, thereby allowing for unscathed passage.  The adventurer will have to use the spell a second time, and the spell is costly, so don't delay.

 

Next, Willow will make his way through a short and simple series of red caves.  Continuing south, he will come across the mouth of a cave.  Just beyond that cave is a bridge that cannot  be crossed at this time.  Inside the cave, Willow will immediately encounter a member of the Eagle Clan called Adik. Adik is searching for his brother, Abang, and asks Willow to take that brother's Wing Sword as identification. The sword is pretty much useless and ceremonial based on the fact it's weaker than the first sword Willow has access to. (Brothers handing out swords called Adik and Abang - sounds like the developers either ran out of ideas for character names (which is kinda lame considering that 98% of all the content in this game is pulled from the film) or they felt the need to implement the obligatory perversion that goes into video game development.)

Further to the southeast in the purple caves, find an old woman who simply states that the bridge is cursed and cannot be crossed.  These caves are quite simple to navigate, so make your way back to the outside and return to the red caves where Willow found an old man that talked about Tir Asleen.  He will provide Willow with a pair of Witch's Shoes, which will allow the adventurer to cross the cursed bridge.

Exit the caves and head east over the bridge to make the way into Tir Asleen.