What is the key to getting tack sharp photos?

Even when I shoot with well regarded prime lenses (35 mm nikkor dx for example) with fast shutter speeds (prefer faster than 1/100) I still only end up with 10% of my photos looking tack sharp at 100% crop.

Is this the fault of AF on my D5500?

Is it because I'm not holding the camera still enough, even at <1/100 shutter speeds?

And really the most important question, is it even possible to shoot tack sharp all of the time, or should I just accept near misses lest I chimp every single photo?

Pic unrelated, an excellent photo posted here several weeks ago.