Use Different Abilities
Unlike the first game in the series Ori is now able to equip various abilities. Ori starts of with Spirit Edge (a sword) and Spirit Arc (a bow). As you earn more Spirit Light, you can unlock Spirit Star (a boomerang), Spike (a spear), and Spirit Smash (a hammer/mace) by talking to Opher the merchant. Becoming familiar with all of these different abilities will improve your chances in combat shrines.