This is a very interesting question, it would appear to the surface mind that to overcome a thing is to face it and fight it with it's opposite.

That would be like Karate: Block and counter the strike.

However there is another way like Jiu-Jitsu: Turn step and help the strike to over strike to the opponent's detriment.

Both are effective but as I remember drilled into my brain by my Sensei "The best block is not to be there."

So if we look at this problem in this way instead of fighting the fear, we simply see there is nothing to fear, the fight vanishes before it ever begins.

If we fear death we will do everything to avoid it and this means our minds will mostly be on avoiding death. That seems okay on the surface mind but deeper if I am a samurai and in a battle doing everything to avoid being killed I will most certainly be killed. Why would that be you may wonder. It is simply that if my mind is not %100 on what is happening at the moment I can not be at my %100 reaction time and response. The more I put my mind on the fear the less my mind is on the battle, in fact I can even freeze up from the fear then that is certain death or the mercy of the opponent to not kill me. When the samurai went into battle they said "today is a beautiful day to die." The American Indians said something very similar, when you release the fear of death the obstacle of death fades away.

When we give up the fear there is no battle to be won, it was all an illusion created in our own minds of a possible negative outcome. In other words our minds played lets pretend and didn't like the results that were imagined. Here is where everything went wrong instead of like a computer working out the best results our minds say "whoa I don't want that so I am not going to try even." Instead it should be more like a maze, "Opps that brought me to a dead end last time. What other choices could I make? I'll try this turn this time." Use that (lets pretend) mind to work out the best solution don't stop at the worst solution but find how to get the results that you want.