There's a great line from the newly released movie The Good Dinosaur:
"Listen kid; You can't get rid of fear. It's like mother nature, you can't beat her or outrun her. But you can get through it. You can find out what you're made of."
That pretty much sums up the reality of fear: it will always be present, to the very end, in varying degrees. So it seems the point is not overcoming fear indefinitely - no; it is a natural, built-in mechanism - but rather maturing through it. Outgrowing it.
Sometimes a good tool is useful. Here is something that might be helpful - a Fear Inventory. It has been used in various counseling situations as a means of writing out and processing our fears. It starts out with naming it, in the first few columns, because without that first step we are only deluding / lying to ourselves. Be honest. You're afraid. But as we progress along we begin to see that somewhere in the fear there is something self-centric, self-preserving - and that we have been turning towards ourselves rather than onto God. We name it - whether it is ambition, self-preservation, pride, self-reliance, or other aspects of the self. These are things we cannot grab at, they are only gifts that God can grant to us in reasonable measure. Were we to grasp at these things as ends in themselves, we would find them like sand, slipping through our fingers. We find as we are letting go of the self, that only then God can gift back and help us to outgrow our fears. So in the end we are directed back towards God, to trust Him, one day at a time, through a prayer, or some kind of action taken.
I hope this tool is helpful. It is only as useful as much as you use it. It is effective when it is practiced, as a tool, often. I myself have written out a fear inventory many a time. I hope with practice, you will outgrow some of your fears, gradually maturing and surely making progress, one day at a time.