Wildlife is very different than capturing landscapes
Eyes in focus
True for animals and anything else with eyes! As a viewer of a photo of a subject that has eyes, YOUR eyes are immediately drawn to the subject's eyes just like you would be when having a conversation with someone. If the eyes are sharp, you will notice that right away. If they are not sharp, you will notice that too and probably conclude "that is not a very good photo".
How to achieve
With a dSLR, you can achieve this by focusing on an area that is either the eye or very close to the eye. With the newer prosumer mirrorless cameras, there is an Eye Tracking feature that can be amazing. Consult your camera manual for details on how to enable this feature.
How to get animal in frame and in focus
There are a number of ways to accomplish this. If the animal occupies a major portion of your composition, try to get the eye in focus (see above). If the animal is only a portion of the composition, you will have to practice, practice in order to achieve your goal. You could try to widen your field of view and crop to your desired composition. With the newer prosumer mirrorless cameras, there is an Eye Tracking feature that can be amazing. Consult your camera manual for details.
Don't cut off legs & feet
For closeups of the animal, this is mandatory. For close to full body compositions, definitely not. Again, practice, practice!
Setting Aperture & Focus
To get maximum bokeh in any shot, set your aperture to the lowest numbered f-stop your lens is capable of. As long as there is some distance between your subject and the background, focus on the subject and shoot.
If your background is close to the subject, you will have to perform some magic in post processing (blur of some sort) to accomplish this.
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