Many a-time I have purchased a air-gun and it had potential,seemed to be accurate,

But the trigger was awful,some could be adjusted better ,others you had to find ways of making it better.I think that a good trigger on a pistol is very important,it is just too easy to "pull" a shot on a pistol.
After pulling triggers tens of thousands of times,it is the the "trigger break" or 'let-off' for me that is most important.
Many guns need time to break in,like the wearing of the moving surfaces ,some triggers are just junk and will never wear-in,that is the time for you to smooth the moving parts.
Many of my Crosmans and Prods can have splendid triggers,the Crosmans can be fixed ,my Prods wear in great.
A trigger finger needs to be trained for feel,your mind,body,trigger integration also must be one.
Sight picture ,trigger pull,breath and follow through,all this comes together is seconds in offhand shooting; using a rest will make things too easy.
Offhand shooting well help you with all the above,it can become frustrating at times,but do not give up,I say this because once you set your butt down on a shooting bench your offhand shooting days well maybe over,..I see my ADD mind has wondered again,another reason shooting for me is such a joy,take aim and shoot ,how simple is that:unsure::ROFLMAO:
 
I can agree with all of the above. One reason I do not have a ginormous collection of airguns is that it takes time (in my case years) of using a gun before I am able to shoot as well as it can. And then there are days where I am just not on my game, no matter how well I can shoot a gun. Those are the days I learn the most. Failure is a great teacher if you don't get emotional about it (something I am not always great at either).
The guns with the best triggers are on my PCPs. The Marauder trigger is (for me) amazing! Best I've used on any gun I've shot after removing the lawyer spring. My Dreamtac trigger is very good as well. Did nothing to it out of the box except rotate the blade a little to the right to match my finger position. And my 1701P trigger is also solid and set up exactly how I like a pistol trigger to break. When I get out the 397PA, I realize what a bear it is compared to the rest. Definitely the worst trigger I own and yet I have taken more game with it than any other gun.
I practice offhand with them all, but the Marauder is really set up best for it. A proper sling really tops it off, but the best thing I ever did to it was getting rid of the scope. It really reminds me of shooting my Ruger 10/22, though a bit heavier. It just has that feel which lets focus on line up and trigger. Simply magical.
Sitting at a bench with any of my guns gets boring fast and really only serves to prove that the gun is shooting well. Offhand, particularly standing offhand, is a challenge. It will change your expectations about what an accurate shot is. Like you said, a lot has to come together at precisely the right moment. You learn to trust your gut a little more. So much of it is feel, connection to the tool. A rewarding experience, even on a bad day.
 
I bought an inexpensive gun some time back. I liked the look of the gun, and I wanted something just to have "out", a kick around gun, that I could pick up and shoot, without digging through the safe.

A black laminated BSA Defiant filled the bill.
Overall, nice looking, a little heavy, but not too bad. Accurate as most, but...the trigger took two fingers to pull ! After messing with it for a while, I figured it was way too tight in its housing. I removed one nylon spacer, and wallah, a nice trigger. It didn't even need any adjusting of the set screws to change the way it worked.

Mike