Usually you’ll find an opening to attack after its second bite attack. When you see it using lightning attacks, stay at a safe distance. If you see it draw back a bit to prepare for a lounge, get ready to roll to the side to avoid the incoming damage. If you try to strafe behind him, watch out for its fast turn and biting attack.
Avoid its fast biting attacks to try to strike it a few times. Halfway through the bridge you’ll find a huge Outrider Beast behind you. You’ll see a bridge as you enter the cold snowy city of Irithyll (you can’t cross the bridge unless you had defeated the Deacons of the Deep).