Yes it is a sniper credo but it also applies to serious hunters. After the first shot in the field or woods, every animal knows. And if your game animal was not hit or vitally hit on the first shot you will rarely have a second shot. Color your animal gone or likely lost!
Ok how to improve?
First only take shots that are within your capability?
How do you know this?
By practicing and learning your limits. The kill zone of heart and lungs of a large whitetail buck for example is 8 inches but a doe is often much smaller and more like a 6 inch kill zone. I keep my shots in that zone when practicing off hand. My max range for off hand is about 50 yards. If I have time to brace against a tree or use shooting sticks, like I did in Africa, my confidence grows to 300 yards or more.
So finding a brace, such as shooting sticks or pods, helps make that first shot count!
When I take a stand and can see longer than 50 yards then I will employ a brace like shooting sticks or a bipod or monopod. My hunt in North Carolina a few years back placed me in a sorghum field with a 380 yard view. I had a spike buck on day three cross the field at nearly 300 yards. You can see my monopod in the photo below.
I had a monopod firmly strapped to my stand and took that spike with my Savage 7mm Rem Mag. I was meat hunting after 3 days of seeing not one deer! If I didn’t have that pod, I would have been forced to pass on that shot. I hit the buck near top of the lungs and he fell like lightening but a moment later it stood and I placed a second shot just a few inches lower and put him in my freezer.
I have a Harris Bipod that is useless in northern NH hunting and the mono-pod walking stick which is nice but I think a larger lightweight telescoping bipod or even the tripod is a better answer, such as the bog-pod by Battenfield Technologies, Inc.
I show this brand because it so well thought out! Check it out at your local sporting goods store.
Make that first shot a kill shot like this Red Hartebeest below taken with bow.