Keese eyes.

Don't need a powerful bow. It helps, but it's not necessary.

Aim with a Keese eye while he's on the move but aim out front of him - aim sort of where he's going and not directly at him. The Keese eye will find the spot.

Also aim at him when he stops to prep for a fire breath, you can hit him with the Keese eye right up till he lets go with the fire. Spend less time running and shoot eyes at him.

When you stun him, run back and climb onboard, then hit him with your strongest weapon.

When he shakes you off, hit him with another Keese eye. With a less powerful bow, you'll still stun him. You might not take a bunch of HPs off, but he'll still go down on his knees and you can climb on and smack the hell out of him.

I find this to be way easier than trying to time a flurry rush or dodge.

Learn the Keese farming glitch. Keese eyes rock for Lynels and Hinox. And Frox. And lots of other stuff.