How to be fearless as Ph.D student?
I'd say that you must learn not to take things too close to your heart. "Fear" appears when something hurts our self-esteem. The key is to realize that in most cases it should not. Say, a reviewer rejects your paper, providing very harsh comments. You feel like jumping between a cold shower and a frying pan, but you should't. Reviewers don't know you personally, they are only doing a job of bashing your paper if it's not good enough. If you paper is not good enough, it doesn't mean that you aren't good enough, so your self-esteem shouldn't suffer. (And it especially shouldn't suffer if a reviewer is wrong.) Accept criticism and continue. 

If you fail, often it means that you aim high, so it is normal to fail. We aren't in school where all problems have ready answers. Many directions are dead ends, and we must realize that it's OK to hit a dead end from time to time.

In a sense, it is equally important to practice humility. A huge number of talented people establish start-ups, record songs, write novels and draw comic strips. Most of them fail, this is just the way it is, and we shouldn't think of ourselves as exceptions. Accept that failures are as inevitable as gravity (so, once again, don't take it too close to heart). It is also useful to understand your limits. We all have stronger sides and weaker sides, and even our stronger sides in most cases won't get us a Nobel prize next year. Aim high, but stay realistic with your goals.

In short, be passionate about your topic, but try to keep your inner self "protected". It should not suffer when you are hurt as a professional (due to failures or criticism). It is hard, but doable to some extent.