Kretos and Kir's battle went on for days. As they continued to fight when there was an opening they would try to eat whatever they could. Sometimes they would eat some insects that were near, if they were lucky a lost bird would come close to them. If one of them wasn't able to eat for a few days, it would mean that the other would gain an advantage.
Aside from food, it was much harder to look for water since their fight had buried the lakes and rivers. It was a good thing that it rained every now and then which was enough for the two. If it were any other demon they might have died after a few days without eating or drinking as their mana was depleting. Yet these two continued fighting without pause as they also tried to salvage whatever food and water they can.