Yes, I know, you've heard this one before: There is no need to fear failure, after all it is a learning tool!
But eliminating the fear of failure takes a lot more understanding and processing than that. In fact, you should thoroughly understand this and then you'll have so much more freedom in your life, plus alot more enrichment and adventure!
THE IMPERATIVE TO WIN!
Our culture says winning (even being #1) makes us worthy, admirable, lovable, etc. and losing is a disgrace or at least a horrendous shortfall, especially if it occurs more than once. And if we lose, then we're not liked or loved (in our minds).
We should redefine winning though as "doing your best, not being the best".
THE IDEA OF A LOSS OCCURRING
SOME "LOSSES" ARE PARTIAL GIVE BACKS OF GAINS
When we "fail" we do not achieve something that we thought we needed or wanted in order to be "OK" in our lives. But, in truth, as long as we are capable of surviving reasonably well in life (eating, shelter, some time for enjoyment), we are just fine. In addition to the link above about "loss", it would be good to Understand And "Get" The Mountain I Have Vs. What I Am Missing.
THERE IS NOTHING TO FEAR IF NOTHING ACTUALLY HAPPENED
In most cases, a few failures here and there will not actually change someone else's opinion of you (of a person who actually can affect your life). Believe it or not, they have already pretty much sized you up and put you in a category of not so good, good, very good, great. You will not lose social status such that it will affect your survival. (See Understanding The Nature Of Social Status.)
In almost all of the situations we are in the actual fear is about something that will not actually affect you at all, so if it happens, relative to you "nothing happened".
THE ONLY THING TO ACTUALLY FEAR
The only thing to fear, for which we evolved, is the loss of survival or limb and a significant impairment to our ability to survive at the base level (i.e. be kicked out of the tribe into the jungle to be eaten alive or starve to death).
DO THE FEAR PROGRAM - THE UMBRELLA OVER ALL OF THIS
Your fear of failure, of loss, of making mistakes, all of those are from the same basic misconceptions and false beliefs as most fears. Most fears are based on "faux" (not real) threats - and they need not occur at all!
The Fear Management Program. Be prepared to do "the work", which is alot, but the reward will be to have your very life back and, for the first time, have the opening for true happiness in life, free of 99% of the fears and "negatives".