After defeating the beasts in the underground, you can climb Mt. Woe.
Prepare
If you have not already done so, you may wish to go back to Algetty and rest at the Inn, and save the game.
Then go back to the north end of the Beast's Nest and walk up the chain where you fought the Mud Imp and Beasts.
Mt. Woe
Change your party to Crono, Ayla, and Robo.
Fight the Rubble to the right if you wish. Rubbles give you a lot of experience and skill points, but they lock all techs so you have to defeat them with physical attacks, and physical attacks almost always miss. Not only that, but runs away eventually. Most of the Rubbles on the mountain will permanently disappear after you fight them.
Go north, battling monsters on the way, and follow the path until you find a chest. Open it to get a Lode Helm. Then go back to where you entered, and go across the chain to the left. Follow the path to the next area.
There is a Rubble to the west that you can battle if you wish. Then go east and north, and you will encounter some Gargoyles.
To the north, there is a difficult-to-see save point. Go north from there, and there will be an enemy encounter. Whenever you are fighting multiple enemies that include Gargoyles, defeat the Gargoyles first. Then go across the chain to the east.
The Rubble here will reappear if you kill it and leave the area and come back, so if you want to level up in a hurry, you can use this Rubble to do so.
Open the chests to get a Lode Vest from the southern chest and a Shield from the northern chest, then go back across the chain to the west. Go west from there, ignore the small slope to the south, and keep going west to reach a chest. You can reach it after an enemy encounter. It contains a Barrier.
Then go east to that small slope to the south and use it to go south. From there, go west and follow the path until you can go north up a small slope. Keep going north and there will be an enemy encounter, and then you can go north and open the chest to get a Lapis. From there, go east across the chain. The path from here is straightforward. It leads to a chain in the southwest. Go south down that chain.
Continue going south if you want to battle a Rubble. Then go north to the chain and go east from there. After a monster encounter, go east and open the chest to get a Barrier. Then go southwest to the short slope, and go east across the chain to reach the next area.
Go north and open the chest to get a Lapis. Go east and cross the chain south of the monsters, then go north to find a chest that contains a Barrier, then go south to find a chest guarded by some monsters. The chest contains a Full Ether. Then go west across the chain, then go north to the next chain, and defeat the monsters that attack.
Go north up the chain, follow the path and fight the Rubble if you wish, then go south if you want a Shield and a Shelter, but you have to fight monsters to get them. Then go north to find a chain that leads east. Cross the chain, follow the path, and defeat the Gargoyles. Go north and use the save point to the right of the chain that goes north. Then go north up the chain.
The path here is straightforward. Just continue along the path and open the chests, which contain a Time Hat and a Full Ether. There is also a Magic Tab in the southeast corner of the area. Go north up the chain.
If you wish to change your party before the upcoming boss battle, do so now. Robo and Ayla work well. Equip everyone with fire-protective gear, such as the Red Mail, Red Vest, and Ruby Vest. When you are ready, check on the block of ice.
Giga Gaia
Kill the hands first, then attack the head. Falcon Hit works well on the hands, and Volt Bite works well on the head. Whenever the hands are revived, kill them again before you resume attacking the head.
After the battle, watch the cutscene.