Four words to describe this fight: Demise is no joke. If you really want a challenge, make sure you play through Hero Mode and take on Demise in the Boss Rush Mode, as you will not be able to use any potions during the fight. The battle between Link and Demise has two phases.
This phase is very simple as all Link has to do is wait until Demise attacks so that he can counter with a shield bash and then strike Demise with his sword. Repeat this strategy and eventually throwing Demise backwards onto his back. The boss will then launch himself back to his feet summoning a lightning storm for the final phase of this extremely difficult battle.
During phase two, Demise will call down lightning to electrify his sword. Once his sword is electrified, he will be able to send a single skyward strike type projectile after Link that is only avoidable by dodging to the side. Taking damage from any other electrified sword attacks is only avoidable by utilizing a well-timed shield bash or dodging; these attacks are unblockable otherwise.
In order to damage Demise, wait until you see lightning striking in the background, raise Link’s sword to electrify it, and slash at Demise. Doing so will stun Demise allowing Link to attack. Note: if Demise’s sword is electrified, he will attempt to strike Link upon seeing Link trying to charge his sword. DODGE this attack or else Link’s sword will lose its charge.
Repeat this strategy until you are prompted to use the fatal blow on Demise to bring this battle to an end.