Don’t try this at home kids. Geryon is pretty difficult to fight the right way, which is a combination of getting on his carriage with Helm Breaker and quickly lining up High Impact when he stops.
You can cause him to fall down by shooting the horse while he’s moving, but he only stays down for a brief moment. It is possible to get him in a bit of a loop in the middle of the stage using High Impact. You actually need to let him slow you down in order to avoid the attack, but if you just stand next to him after knocking him down he should spin his carriage around and end up in the same spot. If you do everything right you can jump over the attack, helm breaker down next to him and immediately High Impact him again.
The Mission 18 fight starts the 2nd phase of the fight with full health. Normally you can take out about 1/3rd of his health in the other phase. The easiest way to do this is to get into a rhythm and try to find a pattern you can exploit. Geryon can either repeatedly dash straight across the screen, do a few loops around (this is when you can jump on for some damage and Devil Trigger buildup), or do a stomp followed by a spinning attack. It seems to all depend on when and where you knock him down.
