Shooting an agitated wild animal ... there is no ace in the sleeve for that.
Any animal from a handgun cartridge will take a few hits and of course you’re not doing weaver stance on them either. You have to slow them down so you can boogie as best you can.
Even a bear with a full mag emptied into it can get you. You will slow it down and retreat some ways before it finally falls.
As mentioned before, these animals will fall because of tendons being hit or muscle being ripped. When that happens, the animal physically can’t advance like it would unhurt.
In the woods carry something with a large capacity. A cat or something fast may take 8 shots just to hit it. They are wiley and hard to hit in the first place. Coyotes hunt in packs so they surround you too. There is rarely only one tracking you and about to pounce. They communicate.
If it’s possible, a small shotgun is a great outdoors protection option. A sawed off Spanish double barrel for instance. You can even holster it.
I have a Sig P-220 in .45 and some 10-round magazines. I don’t know what commercial ammo would make the best of it against a large animal. My Sig is I am sure minimal against a black bear but I can’t carry a rifle or shotgun everywhere. Black bears are a bit overpopulated here so they are something one can realistically worry about.