According to Webster's plain language definition, accomplished means:
very skillful : having or showing the skill of an expert
very successful : having done or achieved many good or important things
If you qualify for the first and have much time in, you'll qualify for the second definition, which is more interesting.
To me, you also have to add ethics and being helpful to others in the sport, especially those who are not as "accomplished." So, someone that shoots deer out from under other hunters or won't take the time to teach his kids or give some good advice to a fellow outdoorsman wouldn't qualify.
I think ethics also involves fair chase, keeping the woods cleaner than you found them, learning and appreciating the whole range of what you see and experience out there and being a credit to the sport, whether it's in conservation or passing along a great sport and tradition that becomes part of who you are as a man or woman.