This is Daffodil Lament by the amazing Cranberries.
After watching the live in London DVD of theirs, i noticed the chords for this song.

Dolores and the guitarist play this song with a CAPO on 3RD.


e|---------------------------------------------------------------------------|
B|---------------------------------------------------------------------------|
G|---------------------------------------------------------------------------|
D|---2-----------------------------------------------------------------------|
A|---2-----------------------------------------------------------------------|
E|---------------------------------------------------------------------------|

e|-----------------------------------------------------------------------------|
B|-----------------------------------------------------------------------------|
G|-----------------------------------------------------------------------------|
D|-----------------------------------------------------------------------------|
A|-------2---------------------------------------------------------------------|
E|---------3-------------------------------------------------------------------|

e|-----------------------------------------------------------------------------|
B|-----------------------------------------------------------------------------|
G|-----------------------------------------------------------------------------|
D|-----------------------------------------------------------------------------|
A|-----------------------------------------------------------------------------|
E|-------2---------------------------------------------------------------------|


And here is the little part of guitar you can hear in the background.
This part uses hammer.

e|-----------------------------------------------------------------------------|
B|---------8-----0------5------0-----3-----0-------1------3-----1----0---------|
G|-----------------------------------------------------------------------------|
D|-----------------------------------------------------------------------------|
A|-----------------------------------------------------------------------------|
E|-----------------------------------------------------------------------------|