It would be best to always have at least one Enchanted Javelin set on the field, Arkana would choose to attack The Unhappy Girl if his attacks would bring your life points down to zero, so having Enchanted Javelin set would most likely stop him after his first attack.
Once you summon Mythical Beast Cerberus, you can start increasing its attack by using Spell Cards. Your target is to immediately increase its attack by more than 2500 so Dark Magician can't surpass it.
On your final turn, leave 1 slot at your back row, set 2 unusable Spell/Trap and put a Field Spell Card. You can then use Storm to destroy all of your opponent's back row cards. This prevents Arkana from using Dark Renewal when you summon Gravekeeper's Vassal.