Figure out which animals apply to your area and move on from there.
For each animal
a big part of this is surprisingly simple. don't attract bears with food odor, don't carry speared fish when in shark country.
The overall risk is very, very low however, keep that in mind.
Those should be the first big things to look into and they are specific to each animal type, so that's why you want to concentrate on the animals in your area rather than trying to figure out a rule for all animals.
Third, if they do go into threat mode or attack, what do you do?
Generally, in BC, Canada, the rule for bears is to avoid confrontation, back out slowly and roll up if they actually attack, covering your neck. A bear is hard to hurt, but is not a carnivore and not really interested in you, except for a mom defending her cubs. (That's not entirely complete, so I've added a bit at the end)
For cougars, it's the opposite. Appear big, wave a stick, possibly throw rocks. If it attacks, fight back. A cougar is a solitary carnivore, if it gets hurt it might starve if it can't hunt, so they will often back down. If it's attacking you, chances are it sees you as prey and your chance to be in that situation because you "surprised it" are low - they're very hard to spot and quite likely well aware of your presence.
Update: having just come back from Cape Scott, with lots of "You're in wolf country" warnings, posted by the park rangers, I can add that wolves here get the same recommendation as cougars: act big, frighten them away, fight back if attacked.
So, each animal has a particular set of best defense advice, but I am 100% in agreement with Ben Crowell that you're best off avoiding an attack situation rather than knowing the defense strategy, which has uncertain outcomes. Still, some quick research about the animals in your location should give some advice, specific to each animal.
Also, if you are still anxious, but want to enjoy the outdoors, you could, after first making sure you first know how to avoid conflicts, purchase a defensive device for the animal. Bear spray, maybe a hunting knife for cougars and a bangstick for sharks. If all fails, you can try your luck with it and it will make you feel safer and more in control the rest of the time. The key thing is that such a device is not an excuse from doing your very best to avoid conflict in the first place.
Finally, some animals are just generally best avoided by not getting into their territory at all, for example crocodiles.
(bears) There's a bit of debate about what to do with them. Mostly people agree not to antagonize them, but... Grizzlies are apparently pretty much never into eating you but can easily kill you without really aiming to. So, play dead. Black bears? Mostly same situation, but could possibly be a predatory bear, which is a very rare occurrence. So an option is to fight back if it keeps on attacking you. Honestly? Seems like if you'd ask 2 experts here you'd probably get 3 opinions about fighting back.
That really goes back to you figuring out the animals you are worried about. Grizzlies have a more limited range than black bears so may not be applicable to your area at all.