Here's my take - I'm new to ear-training and tablature-writing
so this might not be 100%, but sounds ok to me.

(Brackets) mean optional notes, and in chord names means the name 
 of the chord when the optional notes are played.

Feel free to send corrections, and please rate the tab!

Chords:

Dmaj(9dim7) (10) 12 12 11 (0) (0)    or  Dmaj x x 0 3 2 3 (for the intro)

G(dim7)/D   (3)  5  5  4  (0) (0)

Bm(dim7)/D   x   5  4  4  (0) (0)

Bm(dim7)/F#  x   9  9  7  (0) (0)

A(add9)/E    x   7  7  6  (0) (0)

Gdim7/E      x   7  5  7  (0) (0)

Lyrics with chords at the bottom

Here is the picked arrangement, but it also sounds nice and harmonic 
if you strum the full chords at points like the chorus/pre-chorus. 
The intro won't sound exactly the same because I think there's a 
mild delay multiplying the notes to make it sound like really fast 
fingerpicking.

*INTRO*

 Dmaj                                      Dsus4
E|-------------------------------------------------|
B|-------------------------------------------------|
G|--11---------11----------11----------11----12----|
D|-------12----------12----------12----------------|
A|----12----12----12----12----12----12----12----12-|
E|-------------------------------------------------|

OR

Dmaj                           Dsus4
E|--3-------3--------3--------3---4-----|
B|-----2--------2--------2--------------|
G|---3---3----3---3----3---3----3--3----|
D|--------------------------------------|
A|--------------------------------------|
E|--------------------------------------|

THEN
        G/D                             Gsus4/D
E|-----------------------------------------------|
B|-----------------------------------------------|
G|--4----------4-----------4-----------4-----5---|
D|-------5-----------5-----------5---------------|
A|----5-----5-----5-----5-----5-----5-----5----5-|
E|-----------------------------------------------|



*VERSE*
Just like Johnny Flynn said...

   Bm/D    G/D       Bm/F#       A/E 

E|---------------------------------------------|
B|---------------------------------------------|
G|--4-------4------(4)-7-----(7)-6-----(6)-----|
D|----4-------5----------9---------7-----------|
A|------5~------5~---------9~--------7~--------|
E|---------------------------------------------|  x3


*PRE-CHORUS*
This is for, this is for, this is for-

   Bm/D    G/D    A/E    Gdim7/E
E|---------------------------------------------|
B|---------------------------------------------|
G|--4-------4-------6-------7------7-----------|
D|----4-------5-------7-------5------5---------|
A|------5~------5~------7~------7~-----7~------|
E|---------------------------------------------|


-Matilda
                                 
 Dmaj                                      Dsus4
E|-------------------------------------------------|
B|-------------------------------------------------|
G|--11---------11----------11----------11----12----|
D|-------12----------12----------12----------------|
A|----12----12----12----12----12----12----12----12-|
E|-------------------------------------------------|

        G/D                             Gsus4/D
E|-----------------------------------------------|
B|-----------------------------------------------|
G|--4----------4-----------4-----------4-----5---|
D|-------5-----------5-----------5---------------|
A|----5-----5-----5-----5-----5-----5-----5----5-|
E|-----------------------------------------------|


*CHORUS* (SAME AS VERSE)
And she needs you,      this is for Matilda

   Bm/D    G/D       Bm/F#       A/E 

E|---------------------------------------------|
B|---------------------------------------------|
G|--4-------4------(4)-7-----(7)-6-----(6)-----|
D|----4-------5----------9---------7-----------|
A|------5~------5~---------9~--------7~--------|
E|---------------------------------------------|


And she needs you,      this is for Matilda

   Bm/D    G/D       Bm/F#       A/E 

E|---------------------------------------------|
B|---------------------------------------------|
G|--4-------4------(4)-7-----(7)-6-----(6)-----|
D|----4-------5----------9---------7-----------|
A|------5~------5~---------9~--------7~--------|
E|---------------------------------------------|


And she needs you,      this is for Matilda--

   Bm/D    G/D       Bm/F#       A/E 

E|---------------------------------------------|
B|---------------------------------------------|
G|--4-------4------(4)-7-----(7)-6-----(6)-----|
D|----4-------5----------9---------7-----------|
A|------5~------5~---------9~--------7~--------|
E|---------------------------------------------|

OR YOU CAN PICK FASTER LIKE THIS FOR SOME TEMPO 

E|---------------------------------------------|
B|---------------------------------------------|
G|--x------x------x---------3 times------------|
D|----x------x------------per chord------------|
A|------x------x----x--------------------------|
E|---------------------------------------------|
 -a
 Dmaj                                      Dsus4
E|-------------------------------------------------|
B|-------------------------------------------------|
G|--11---------11----------11----------11----12----|
D|-------12----------12----------12----------------|
A|----12----12----12----12----12----12----12----12-|
E|-------------------------------------------------|

        G/D                             Gsus4/D
E|-----------------------------------------------|
B|-----------------------------------------------|
G|--4----------4-----------4-----------4-----5---|
D|-------5-----------5-----------5---------------|
A|----5-----5-----5-----5-----5-----5-----5----5-|
E|-----------------------------------------------|






*LYRICS + CHORDS*

*ACAPELLA*
This is from, this is from
This is from Matilda

Dmaj(9dim7) G(dim7)/D

*VERSE 1*

Bm(dim7)/D         G(dim7)/D
         Just like Johnny Flynn said
              
               Bm(dim7)/f#    A(add9)/E
The breath I've taken and the one I must to go on

Bm(dim7)/D           G(dim7)/D
         Put the grenade pin in your hand, so you 

Bm(dim7)/f#       A(add9)/E
understand who's boss

Bm(dim7)/D  G(dim7)/D        Bm(dim7)/f#       A(add9)/E
     My defeat sleeps top to toe with her success

*PRE-CHORUS 1*

   Bm(dim7)/D  G(dim7)/D
Oh, this is from, 

A(add9)/E Gdim7/E
this is from, 

Gdim7/E            Dmaj(9dim7) G(dim7)/D
this is from Matilda

*CHORUS 1*

Bm(dim7)/D  G(dim7)/D  Bm(dim7)/F#     A(add9)/E
   And she needs you,   this is from Matilda

Bm(dim7)/D  G(dim7)/D  Bm(dim7)/F#     A(add9)/E
   And she needs you,   this is from Matilda

Bm(dim7)/D  G(dim7)/D  Bm(dim7)/F#     A(add9)/E
   And she needs you,   this is from Matilda

Dmaj(9dim7) G(dim7)/D

*VERSE 2*

Bm(dim7)/D         G(dim7)/D
         Just like Johnny Flynn said
              
               Bm(dim7)/f#    A(add9)/E
The breath I've taken and the one I must to go on

Bm(dim7)/D           G(dim7)/D
         Put the grenade pin in your hand, so you 

Bm(dim7)/f#       A(add9)/E
understand who's boss

Bm(dim7)/D  G(dim7)/D        Bm(dim7)/f#       A(add9)/E
     My defeat sleeps top to toe with her success


*PRE-CHORUS 2*

   Bm(dim7)/D  G(dim7)/D
Oh, this is from, 

A(add9)/E Gdim7/E
this is from, 

Gdim7/E            Dmaj(9dim7) G(dim7)/D
this is from Matilda

*CHORUS 2*

Bm(dim7)/D  G(dim7)/D  Bm(dim7)/F#     A(add9)/E
   And she needs you,   this is from Matilda

Bm(dim7)/D  G(dim7)/D  Bm(dim7)/F#     A(add9)/E
   And she needs you,   this is from Matilda

Bm(dim7)/D  G(dim7)/D  Bm(dim7)/F#     A(add9)/E
   And she needs you,   this is from Matilda


Bm(dim7)/D       G(dim7)/D         Bm(dim7)/F#
        Elle a besoin      de----- toi

                A(add9)/E
Cela vient de Matilda

Bm(dim7)/D  G(dim7)/D  Bm(dim7)/F#     A(add9)/E
   And she needs you,   this is from Matilda

Bm(dim7)/D  G(dim7)/D  Bm(dim7)/F#     A(add9)/E
   And she needs you,   this is from Matilda

Bm(dim7)/D  G(dim7)/D  Bm(dim7)/F#     A(add9)/E
   And she needs you,   this is from Matilda

Bm(dim7)/D  G(dim7)/D  Bm(dim7)/F#     A(add9)/E
   And she needs you,   this is from Matilda

*OUTRO (Picked)*

Bm(dim7)/D Bm(dim7)/D Bm(dim7)/D Bm(dim7)/D 



Bm(dim7)/F#       A(add9)/E       G(dim7)/D G(dim7)/D
          This is from      Matilda

Bm(dim7)/F#       A(add9)/E       G(dim7)/D G(dim7)/D
          This is from      Matilda

Bm(dim7)/F# A(add9)/E       G(dim7)/D  G(dim7)/D
                     Matilda, 

Bm(dim7)/F# A(add9)/E       G(dim7)/D  G(dim7)/D
                     Matilda, 

Bm(dim7)/F# A(add9)/E       G(dim7)/D  G(dim7)/D
                     Matilda, 


*THEN THIS FIGURE* (not sure if this is the actual ending, but I like it..)

@x@ means natural harmonic at that fret (I don't know the proper symbol)

  G(dim7) with thumb on Low G (for E string harmonic) 
  or regular G barred (355433)
E|---------------------------|
B|---------------------------|
G|-4------4--------@16@------|
D|---5------5----------------|
A|-----5~-----5~-------------|
E|---------------------@15@--|

Thanks for looking!
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