I wouldn't call him the "most broken champ ever." I mean, beta TF had a 2 second targeted AoE stun on a 4 second cooldown, gave his entire team free crit chance, had a global teleport on a basic ability, and a global slow that also made his global teleport instant and revealed everyone. But nah, Kayn's mobility is so broken because he can move through walls for all of 5 seconds (1 if someone even so much as damages him, not long enough to get through anything but the shortest walls in the game, and if he gets stunned, it instantly cancels) is the most broken champion ever to exist. Oh, and don't even get me started on AP Yi seasons 1-3 or Yi in general before then (his ult was his current Q but with 10 bounces and a 300% AD ratio because fuck your whole team).
You wanna beat Kayn? Here's how: first off, dodge the dash part of his Q. It deals damage on both the dash and the slash, same damage, so if you dodge the dash part, it does half damage. Second, dodge the W. Regardless of form, this ability is strong. Third, now he's gonna auto you and ult you. Stun him and walk away before he can auto you and you're fine.