I have read and understood or developed some different hunting strategies and these are the ones I know of:
1. MM, all animals except bears
Shoot an animal over a river/cliff. Deaggro when it runs. When it has stopped running, go up close to them and shoot again.
This works with all animals except bears because of their rage mode when they get to low health.
2. MM & UA, boars
Shoot a boar over a river/cliff. When it runs, run after it on 3rd speed and punch it till it dies. Be aware of tusk romp.
Alternatively start with UA immediately instead of MM. If you have low UA this is still possible by attacking it over a cliff and making sure to stay away from the cliff when the boar twitches (tries to move) at you.
This works only with boars since they are the only animal you are faster thatn at 3rd speed.
3. MM, bears, group
One person aggroes a bear over a cliff and the other(s) surround it with stockpiles, roundpole fences or anything which can keep it contained (do this at 1st speed, crawl, to avoid aggroing the bear). When the bear is enclosed you can safely shoot it until it dies without it being able to run away and without having to fear for rage mode.
This works with all animals but is only necessary with bears.
4. MM, bears, solo
You need to find a good spot for this where the bear is enclosed by water on many sides and you will probably need a river as well as a boat.
Example:

Now all you have to do is shoot the bear and deaggro it as in strategy 1, but make sure to always stand next to your boat. When the bear enters rage mode, jump in your boat and go to the other side of the river. From here, shoot the bear till it dies.
Now I feel these are all fine methods of hunting, but I don't really enjoy the chasing part.
I would also like to hunt all animals with UA, not just boars. The problem is, all other animals are too fast to catch up to when they flee so I can't see how It's possible to kill them without either shooting them or having to chase them for a VERY long time.
So I would like to know your hunting strategies, tips and tricks.
Happy hunting!