These caves require a bit of exploration as well as combat to get through each lair of the caves.
A Grappling Claw is required to complete all of these caves, this is acquired very early in the game from Wogah, so you may have to advance the story further with him if you have not yet unlocked it.
Make sure to stock up on Animal Fat; this allows you to light your weapons without having a static source of fire nearby. You can conserve the amount of fat you use by lighting an object nearby on fire, allowing you to light future weapons from that. Small campfires work best for conserving your flame.
Falling into water extinguishes your fire. Try throwing your lit weapon across the water into some objects so that you can light your weapon again without using fat.