The problem with having a irrational fear of failure is that in many ways its also a fear of being inadequate - that is, that the reason you're failing is because you're not good enough. So having a fear of failure naturally means that you might try things less, because that way you're less likely to see that perceived inadequacy. In essence, as with many fears, it's about removing an uncomfortable feeling.
The key to overcoming fear of failure is to become comfortable with it. It sounds weird at first, but it's natural if you think about it. If humans aren't perfect, then by definition we all have flaws and make mistakes, and thus 'fail' in some way. You're not going to get 100% every time, so don't let the chance of failure deter you from the chance of success and growth. You might not feel inadequate and anxious if you don't try things, but you also miss out on growing as a person and learning more about yourself and the world. There's lots of info online about how to be comfortable with failure - defo recommend you check that out, I think it would really help you out x