I think for most people, the biggest fear is probably that not that you will make a mistake, or not play as musically as you wish, but that you will forget where you are and have to stop the piece. To be less fearful, you have to know that you really know the piece. If you can visualize both hands (away from the music or guitar) in tempo, then you know the piece. If you can write out the music from memory without the guitar, then you know the music. If you know that you have not only muscle memory, but additional memory chains as evidenced by the ability to do the above activities, then you will not be concerned about forgetting the piece. You will also be training your mind to stay focused completely through the piece. In my experience, losing your train of thought is the culprit, because when you come back into focus, you have already broken the muscle memory chain.
2011 Traphagen Cedar Doubletop
2017 Traphagen Spruce Doubletop