Is there any real need to kill all of the Divine Beasts before going on to fight Gannon? I stumbled into Hyrule Castle and it seems like I can go ahead and start the fight. I’ll need more health and weapons, but is there any need to kill all Divine Beasts before fighting Gannon?
You do not need to kill all of the Divine beasts, but It is a good idea to do it for 2 reasons. First is that you will get a unique ability for killing each one of them. Some are better than others, but I used Revalis Gale to get past a lot of enemies on the lead up to the castle door. The second advantage is a bit of a spoiler, so beware!
Minor Spoiler Ahead – When you kill a divine beast it will shoot a sort of laser over to the castle. When you begin the battle with Gannon, these lasers will all hit him and damage him. I entered the fight with all 4 beasts killed and it took away half of his health. It is a tough enough boss fight, so having half his health gone was a major advantage.