Don't forget to use all your various abilities and items. You should be able to clear the cave at level 4-5!
I'll say there's a useful magic ability you can use against slime foes, that you may have missed. If you have any old saves from back in the blue slime forest... there's a certain person you can rescue, and they'll give you an item that works as a 'key' to access an area with a useful spell!