Unarmed uses very little stamina which makes it good in some situations. You can quite easily beat the first 3 biomes without weapons but a good unarmed skill. It will take longer than with weapons tho, so I don't recommend it.
If you want to level unarmed just kill the elder or bonemass with fists. Bonemass will die quickly with a high unarmed skill tho, fists do blunt damage.