When facing Dario for the first time, have a weapon that does a great amount of damage (for example, the Death Scythe). When hit with the weapon, he will be knocked back and stunned. Hop in the air and attack again while in the air. You will still hit him and be able to hit quicker. Back him into a corner and keep hitting him. He will soon die. Note: It all depends on how much damage you do. The higher the strength, the better chance of knockback.
To kill Dario the last time you fight him, make sure you have the Puppet Master Soul. When Dario shoots his fire snakes and you are trapped in them, use the Puppet Master Soul to get behind him and keep attacking. Note: Using the Golden Axe from the souls helps a lot.