These fights only take place if you skipped the Divine beasts (like Any%). The Blights are stronger forms of the original dungeon boss fights. Each fight is divided into two phases.
In the second phase of the fight, Calamity Ganon surrounds himself with a shield, making him pretty much invincible until the shield is down. Luckily it is possible to permanently stun lock him with a precise timing on the hits. To kill him, reflect one laser to get the shield down, then perfomr the stun lock as seen below.