GOTTA= (col.) [everybody's] got to, (they) must.

RISE FROM THE ASHES= Have a new life after being destroyed and shattered.
This image is taken from the ancient legend of the mythical Phoenix /fi:nɪks/. It is a colourful eagle-like bird who had a life-cycle of 500 years. At the end of each cycle it builds itself a nest and then the nest turns to flames, consuming the phoenix and turning it to ashes. From the ashes, a new young phoenix arises, reborn anew to live again for another cycle. For this reason, the phoenix has long been presented as a symbol of rebirth, immortality and renewal. In this song, the symbol of "rising from the ashes", as the phoenix does, is used to talk about recovering from a bad time or depression with renewed energies, ready to come into full life again.

ACHE= /eɪk/ pain.

GIVE UP= Surrender, stop trying.

YOU GOTTA= You have to (see above)

FACE= Confront. The opposite of facing something is hiding from something, elluding it, ignoring it  or running away from it. If you have a problem ("the clouds" here) you can either face it, confront it, or forget about it, do as if that problem doesn't exist. Only by facing that problem can you solve it, only by facing the clouds can you find the silver lining they carry inside.

TO FIND THE SILVER LINING= This is a reference to the popular proverb "every cloud has a silver lining", which means that there is always something good even in bad things and we must be optimistic and "look on the bright side of life".
The "lining" /laɪnɪŋ/ is material used to cover the inside surface of something. For example, a coat may have a warm fur lining in the inside to make you warmer. In Britain, weather is terrible, clouds are in the sky almost permanently, so a cloud is a negative thing for them. The idea that every cloud has a silver lining, that is, that there is something wonderful (silver) inside of those nasty nagging things (clouds) is a good image to show that you can find good things even in bad things, there is hope.

WHEN THE SKY IS FALLING= Ever since the ancient Celts were terrified at the idea that the sky might fall down on them (remember Asterix), this idea has been used in Britain to represent those times when your whole life crumbles and you fall into chaos and despair.

BRAND NEW= Completely new.

SCARED TO DEATH= If you are scared to death, you are very very very scared, you are terrified.

TO TAKE THAT STEP OUT ON THE WATER= A symbol sometimes used to talk about true faith. This image is taken from Matthew 14:22, where Peter's faith was put on the test. This is the passage:
Immediately Jesus made the disciples get into the boat and go on ahead of him to the other side, while he dismissed the crowd. After he had dismissed them, he went up on a mountainside by himself to pray. Later that night, he was there alone, and the boat was already a considerable distance from land, buffeted by the waves because the wind was against it. Shortly before dawn Jesus went out to them, walking on the lake. When the disciples saw him walking on the lake, they were terrified. “It’s a ghost,” they said, and cried out in fear. But Jesus immediately said to them: “Take courage! It is I. Don’t be afraid.” “Lord, if it’s you,” Peter replied, “tell me to come to you on the water.”
“Come,” he said. Then Peter got down out of the boat, walked on the water and came toward Jesus. But when he saw the wind, he was afraid and, beginning to sink, cried out, “Lord, save me!” immediately Jesus reached out his hand and caught him. “You of little faith,” he said, “why did you doubt?” And when they climbed into the boat, the wind died down. Then those who were in the boat worshiped him, saying, “Truly you are the Son of God.”

KEEP (+ -ing)= Continue.

OVERCOME= If you overcome an obstacle, you are victorious, that obstacle can't stop you.

THE ODDS= The chance of success or failure. If you do something against the odds, or you overcome the odds, you succeed even when everything looked against you.

YOU DON'T HAVE A CHANCE= It is impossible that you will succeed (nevertheless, faith will help you "overcome the odds" and succeed)

IT'LL= Faith will... (this IT refers to FAITH as opposed to the world, people)