This is video #15 in my playthrough of The Legend of Zelda: A Link to the Past for the SNES. Link reenters the Dark World through a teleporter between the Lost Woods and Kakariko Village. It is accessible from the north side with the Magic Hammer.
The Skeleton Forest is the counterpart of the Lost Woods in the northwestern Dark World. The third dungeon, Skull Woods, is located here. In fact, it has three sections and numerous entrances. The "3" on the map denotes the entrance to the final section, where the boss is located.
The first entrance that Link uses is a hole directly northeast of the entrance from the teleport tile (time 0:42). Great, more Hardhat Beetles. Link heads south and through the door to the east.
Before grabbing the chest north of the fire bar, Link heads through the doorway to the north (time 1:59). There are Gibdos and a Stalfos here, but they are trapped behind skull pots. Just watch out for the Wallmaster, which will take Link back to the entrance if it grabs him. The northwest chest contains the first Key. The door to the east leads to an entrance from the forest.
Back in the room to the south, Link grabs the Compass from the chest (time 2:55). However, this also makes holes appear, so be careful. Link then heads to the room to the east, which is overrun with traps, bumpers, Gibdos, and a persistent Wallmaster. The center chest contains a Key.
Through the locked northeast door, Link will find the room with the Map (time 4:05). He will have to trigger the first star switch to open the chest safely. To the west, Link exits the dungeon for now.
Outside, he travels through the ribcages to the northwest so that he can reach another dungeon entrance (time 5:02). This is the central section of the dungeon. Baris, Gibdos, and a Wallmaster infest the entry room. After taking out the normal enemies, Link will have to pull a statue onto the switch to weigh it down so that he can go through the northern door.
The room to the north has Stalfos, a red Bari, a Gibdo, and a Wallmaster (time 6:07). The chest contains the dungeon's Big Key.
After collecting this, Link leaves the dungeon again. East of the ribcage tunnels, the center bush hides a hole leading into the eastern section of the dungeon (time 7:43). He lands safe in a ring of skull pots near a Helmasaur and a Hardhat Beetle. The cracked wall to the west can be bombed through. He should trip the uppermost star switch before going through.
In the room to the west, he has to pull on a switch to blast open the southern wall (time 8:31). Past some Mini-Moldorms, he finds a big chest containing the dungeon's hot treasure, the Fire Rod. This will defeat certain enemies in one shot, such as red Baris and Gibdos, but it also eats up magic.
After collecting this, Link is done with the eastern section of the dungeon. He heads through the ribcage tunnels again and reenters the central of the dungeon (time 9:27). He then goes two rooms to the west. A Key can be found under the northwest pot (time 9:54).
For ease, you can now proceed to the final section of the dungeon. For completion, I will go around to the final entrance to the dungeon. Past some tunnels to the north, east, and south, there is a hole leading to the north central room of the dungeon's central section (time 10:22). The star switch in the middle will rearrange the holes in the floor.
In the southwest room, Link can now enter the locked door (time 11:01). There are three Helmasaurs, and the floor around the central sections will fall away shortly after Link enters. After grabbing the treasures here, Link leaves through the southwest exit.
The entrance to the final section of the dungeon is in the northwest corner of the forest (time 12:04). To enter, Link has to shoot the gross tongue extending from the dungeon entrance with the Fire Rod. If he gets here with at least one Key, he can go ahead through the locked door to the north. If he does not, he will need to go downstairs and thread his way to the northeast door to the room to the east. There are Gibdos and spike traps in the eastern room. The southwest door from the eastern room leads to the first room's chest, which contains a Key (time 13:29).
Armed with the Key, Link heads through the northern door in the first room (time 14:07). This room features Baris, a Wallmaster, and a sort of maze requiring the use of star switches to get around to the eastern door.
The hall to the east requires the lighting of four torches (time 14:53). After clearing out the mummies, it is most expedient to use the Fire Rod to light the torches. It is required for the northernmost one.
The northern exit to the west leads to a room with a Gibdo and Mini-Moldorms (time 15:44). The exit is hidden behind some vines in the center of the northern wall. In the room to the north are a Hardhat Beetle, a Gibdo, a Mini-Moldorm, and a Helmasaur. The Gibdo holds the Key.
Description continued in the comments.