Mountain lion is one critter I haven't had attack my coops and run. (So far) When you're dealing with major predators, it really can be quite daunting if you've suffered an attack because you were unprepared, and the varmint keeps coming back, and you are behind the curve because you haven't figured out a way to protect against them yet.
Big cats will jump on the sides of the pen and coop, trying to find a vulnerable spot. In my case, it was a gate that didn't have a good latch/lock, and the gate swung open after the big bobcat jumped on it, the chickens all fled, and it nabbed the oldest and slowest one. When the cat came back a few days later (they always return), I got a chance to observe it circling the pen, jumping on the fencing every few feet, looking for a way in.
In the case of bears, they will demolish the infrastructure, trying to get at the chickens. The only way to protect against them is a hot wire with peanut butter at intervals. I sure hope you don't have any. They're the worst predator there is to deal with.
All of the large predators will attempt to climb the fence - a good argument to get the pen covered with a secure material.
Trust me, it's much better to anticipate predators and prepare ahead for them, than to be unprepared and lose favorite chickens. In the case of most predators, they probably won't keep returning if they're unsuccessful at penetrating your defenses on the first try.