It'd be pretty awesome if being a Christian meant a total eradication of all trepidation and anxiety about one's own mortality, but that's not how that works. Christians are still people, and that means facing one's own mortality is still not easy.
Also, it's not about being "good", though Christians ought to live just, pious, and godly lives in accordance with God's will; but we're just as sinful as anyone else. The Christian hope is not that one has been good enough; but that God is merciful, and in Christ God reveals Himself as merciful--who forgives us our sins and who calls us to a life found in Him. That life in God, based on Jesus Christ and trust in Jesus, we believe is the basis for our future life. That even as God raised Christ from the dead, so He will raise us up from the dead. And since we believe Christ has destroyed death, then we do not have to look at death with hopelessness and despair--for God will raise us up even as He raised up Christ.
But faith isn't easy. Even the most devout person experiences the ordinary anxieties and sufferings of this life--and that includes looking at death as it approaches us, and finding ourselves with uncertainty, trepidation--even as we believe that we shall pass through death to life.
Faith is not a joyride to coast through this life. It is an invitation to look at everything differently--to look at everything on the basis of what God has done in and through Jesus. And that invitation comes to us throughout our lives, each day we are called to trust in God, each day we are called to follow Jesus, each day we are called to repent, to change our ways, to change how we think and see the world. Faith in Jesus is not an easy way, but a hard way.
-CryptoLutheran