A walkthrough for Call of Duty : Black Ops – Redemption
by Kenneth Stubbs (OmegaMustard) 

Redemption
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You start in a helicopter assaulting a ship.  You will have a machine gun
and rockets.  As soon as you gain control, sway back and forth and shoot
the targets.  Make your way down the ship shooting all target markers. One
of your squad helicopter will drop a sqaud down on the ship.  Protect them
by mowing down the targets that try to attack your squad.  Take out all the
enemies leading down the ship.  Once you get to the other end, you will be
attacked by an enemy helicopter.  Fire rockets and keep your machine gun on
it and it will fall after a few hits.  Now make your way to the end of the
ship and jump out the helicopter.  Make your way down the right side of the
ship.  You will be attacked by a few enemies, shoot them and keep going. You
will be attacked by two helicopters. 

Intel – It will be to the left a little before the rocket launcher near
        the big crate that you can walk through.

Pick up the Valkerie rocket and shoot them.  If you hit them both with one
rocket, you will get an achievement/trophy here.  Once they are taken out,
pick off the enemies up ahead and move up.  Another group will run out the
door up ahead.  Kill them and the guy up on the upper left catwalk.  Now
make your way in the building on the left. Go down the mini hall and go
left down the two cases of stairs. Kill the guys in the swim suit room. 
Go down the next two cases of stairs and clear out the mini control room.

Intel – Right when you enter the mini control room, it is under the middle
        table.

Go through here into the giant pump room.  Kill the guys around the room.
Make your way around the room once its clear.  On Veteran difficulty, I
found it easiest to go up around the left upper side of this room.  Make
your way around picking off enemies until it says objective complete.
This will trigger some talking and you will then submerge down to the
broadcast station under the boat. 

Swim up inside the ship.  You will be attacked when you come up, shoot the
soldiers and move up to the next piece of the room.  The missile looking
thing will fall down and a guy will attack from the catwalk up above.  Take
him out and move up.  Three guys will run out the door in the back left.
Take them out and go through the door.  When you come through the door, on
the stairwell on the left a guy will come walking down.  Shoot him and
go up the staircase.  Two guys will be guarding the door at the top of the
stairs. Go through the door at the top of the stairs and immediately on the
left there will be two guys hiding behind some crates.  Kill them and go
down the hallway and you will see guys through the door on the right. Wait
outside the room on the left of the door and the two guys will run out.
Take them out and enter the room.  An explosion will knock you back and
now the place will be flooded.  Swim to the marker and climb up on the
catwalk. Follow Hudson to the next room.  Kill the two guys that run at you
shooting dual wield pistols.  Continue down the hall and when you turn left.
You will run into two enemies hiding in the room up ahead.  Take them out.
A well timed grenade will clear the room.  Make your way to the room and
climb up the ladder.  You will come up into a room full of weapons.  Pick
your poison and then make your way down the hall. Two guys will walk around
the corner on the right.  Take them out and continue down the right hall.
Stay to the left side so when the guys in the next room spawn, they can’t
shoot you. Kill the guys in the flooded control center and make your way
in.  Make your way around the left side of the computers and two guys will
run in.  Kill them and then head upstairs.  Kill the guy ducking behind
the desk and throw a flashbang to the opposite wall.  Now crouch walk to
the end and kill the two guys that you just flashbanged.

Intel – Pick up the intel from under the desk in this little room.

A guy will probably run through the door where you just killed the two guys.
Take him out and finish picking off the enemies on this top floor.  Now make
you way to the terminal and activate it.  This will cause an explosion and
you will grab an enemy and pull him down with you.  Press the on screen
instructions to choke him out.  Now make your way off the ship.  You will
then flash to swimming in the ocean.  Just follow Hudson and this will
end the level.

Source :The Call Of Duty Black Ops Walktrough FAQ