Two schools of thought on accuracy with a single bullet:

#1) take a deep breath, let it halfway out and slowly squeeze the trigger until it surprises you.

#2) Plan on a lot of range time where you can shoot the gun effectively enough that your eyes do not even close when the gun goes off. You are comfortable with the guns recoil and know the trigger pressure / creep exactly. Then you can depress the trigger to the point that you know any additional pressure will cause the gun to fire. At this point, you can put the sight exactly where you want the bullet to hit and "slap" / touch the trigger. This method is a favorite of snipers as they have to send the bullt accurately, at a specific time and point of impact.

If you choose #2, I would recommend getting a snap cap for your gun. This way you can become familiar with the trigger pressure / creep by dryfiring the gun into the cap. This will save you wear and tear on your firing pin. In either method...practice, practice, practice.

When you aim at a deer, aim where you want the bullet to exit on the opposite side. Example, on a quartering away shot from a treestand, go through the vitals and exit low through the opposite side frint shoulder. I have made poor hits on deer even though my impact looked good, but I did not take into account the animals orientation. Aiming for a spot you want the bullet or arrow to exit helped me.