I know that everyone has tabbed the crap out of this song, but this is the correct key 
and fingerings to match the actual song.

Chords:

Db:  6 5 4 4
Abm: 5 3 4 2
F#:  3 1 2 1

Intro:
A| 4--4----|2--2----|1--1----|1--1---- |
E| --------|--------|--------|-------- |
C| --------|--------|--------|-------- |
G| --------|--------|--------|-------- |

A| 4--4----|2--2----|1--1----|1--1---- |
E| 4--4----|4--4----|2--2----|2--2---- |
C| --------|--------|--------|-------- |
G| --------|--------|--------|-------- |

A| 4--4----|2--2----|1--1----|1--1---- |
E| 4--4----|4--4----|2--2----|2--2---- |
C| 5--5----|3--3----|1--1----|1--1---- |
G| --------|--------|--------|-------- |  x2

Most of the song repeats this pattern:

   Db       Abm      F#       F#
A| 4--4----|2--2----|1--1----|1--1---- |
E| 4--4----|4--4----|2--2----|2--2---- |
C| 5--5----|3--3----|1--1----|1--1---- |
G| 6--6----|4--4----|3--3----|3--3---- |

At verse 5 ("I've been swimming..."):

A| -4--4---|-2--2---|-1--1---|-1--1--- |
E| -4--4---|-4--4---|-2--2---|-2--2--- |
C| 5--5----|3--3--3-|1--1----|1--1--1- |
G| --------|--------|--------|-------- |

You can repeat this pattern for the rest of the song, or return to the regular pattern 
after verse 5.

Whale, swim with me whale
We will go far into the sea
You will take me onto your back
Never look back, never look back

Whale, sing to me whale, sing me a song
Tell me that things will never go wrong
Hide me away, don't let them stay
Don't let them stay!

Whale, come with me whale
We will go far into the blue
I will take you
Listen to me, then you will see
Then you will see

Whale, don't worry whale,
Just do as you please
I will accept if you'd rather leave
I'll open my heart if you open your heart
Open your heart

I've been swimming for a thousand years and I've
Seen more than you can realize
But I accept that you will never understand
So I will gladly take your hand

Whale, come with me whale!
We will go far into the blue
You will take me
Onto your back
Never look back

Never look back
Never look back
Never look

WHALE! come with me whale
We will go far into the blue
I will take you
Listen to me, then you will see
Then you will see

Whale, don't worry whale,
Just do as you please
I will accept if you'd rather leave
I'll open my heart if you open your heart
Open your heart.