A Tai Chi master is when the practitioner no longer has to ask what's right, or think about movements, as the movements have become a part of them. Their physical movements work in perfect harmony with their internal energy, so even if they see a set of moves or striking methods etc, they don't need to be shown how to move their body, as when it comes down to mastering movement, there is only one way of doing something to gain maximum effect in the martial art.
It takes many many years to achieve this level, 10 years minimum. Many never get there, due to thinking that they are there before they really are, this is due to ego, they no longer want to listen to anyone else as to what they should be doing etc, this just ends in their training getting worse and worse. Also some people just don't put in enough training, as they're doing their Tai Chi as more of a hobby, this is fine, as they get what they want out of it.
You're teacher will have a great effect on how you progress as well. If you have access to train directly with the master of a system, you will advance at a much faster rate. Erle Montaigue (Founder of the WTBA) was awarded his Masters degree in 1985 after about 17 years of training. When Erle Died in 2011 his son Eli (Head of the WTBA, Lineage holder of the Erle Montaigue Fighting/Healing system, and the Old Yang Style) after training properly for only about 11 years was at a much higher level of practice than Erle was in 1985.
This goes to show what a difference it makes having the right teacher, even though Erle trained with the Master of the system, there was a language barrier, and of course he did not have every day live in training as Eli did. So the best way to work towards mastering Tai Chi, is to get as much hands on time with one as you can. The most important thing is to see the Master moving, and to feel his energy. Being close friends will help as well.
A Tai Chi Master should befriend his students, and not think of themselves as better than anyone else. A lot of so called masters have their students call them master, why can't they just call their teacher by their name? When someone bows to a true master and calls them master, the master will push their head back up and tell them that they are a Master of Tai Chi, and not your master, they are your friend. If you knew a music teacher, or builder that had a masters degree in that art, you wouldn't call them your master. A true master of Tai Chi should treat his students as equals, sure he/she will know more about Tai Chi, but in life they treat everyone as equals. A Tai Chi Master should do everything they can to progress the training of their students, and not hold back anything, as some do, so that they will always be better than their students. When the student punches the teacher in the face, (in training) The teacher should applaud them for doing a good job, and be proud, as they are the one that's given them the ability to get that shot in.
A master should never need to show off in a way of bullying his students. They should not feel the need to hit someone hard to show how tough they are.
The master will always walk away from a fight, unless there is no choice, in which case he/she will also have no moral issue with killing someone to protect his family. And will have the skill to do it. Though a master is not super human, no matter how good you get, you can't stop a good fighter with out hurting him, you can't stop bullets, and you can't take on 20 guys and win.