Hey just did today, actually not as hard to transcribe as i thought but Corey's solo is 
pretty difficult, anyways i think this is almost 100% correct.

Legend:
b: bend eg. 9b11: bend from the 9th to the 11th fret
b1/4: bend the string a quarter step
r: release bend eg. 11  r9 release the bent 11th fret down to the 9th fret
~: vibrato
\: slide up
/: slide down
h: hammer on
ph: pinch harmonic
p: pull off
wf: whammy-bar fling eg. (12): the 12th fret is sustaining. as it is sustaining, whack 
whammy bar to get a gargling sound. Look at John Petrucci playing the solo to Under A 
Moon on youtube


Solo 1: Matt Heafy
let notes ring from 1. - 2.
                                                                      1.
E---------------------------------------------------------------------------|
B---------------------------------------------------------------------------|
G---------7--7b1/4------------9b11--9b11--r9~~~~------------7--7b1/4------9-|
D---7-8-9----------9~~~~------------------------------7-8-9----------9-7----|
A---------------------------------------------------------------------------|
E---------------------------------------------------------------------------|

                    2. bend these slowly
E----------------------9b10~~~~-10b12~~~~-12b14r14--------------------------|
B------------14~~~~---------------------------------12~~~~------------------|
G--11~~~~----12~~~~---------------------------------------------------------|
D--8~~~~~----11~~~~---------------------------------------------------------|
A---------------------------------------------------------------------------|
E---------------------------------------------------------------------------|


E--\10---7------------------------------------------------------------------|
B-----------10--7--------10--7----------------------10------7---------------|
G------------------9--7---------9--7-----------------9b12r9-7-----9---------|
D-------------------------------------9--7--9~~~~--------------8------------|
A---------------------------------------------------------------------------|
E---------------------------------------------------------------------------|

   bend slowly
E--9b10~~~~-----------------------------------------------------------------|
B---------------------------------------------------------------------------|
G---------------------------------------------------------------------------|
D---------------------------------------------------------------------------|
A---------------------------------------------------------------------------|
E---------------------------------------------------------------------------|


Solo 2: Corey
E-------------14-19p14-19-17-15---------------------------------------------|
B-----------15------------------19-17-15------------------------------------|
G---------16-----------------------------18-16-14---------------------------|
D-------16----------------------------------------17-16-14------------------|
A--14h17---------------------------------------------------17-16-14---------|
E-------------------------------------------------------------------17-15---|

                 this bit is harmonized
E---------------------------------------------------------------------------|
B---------------------------------------------------------------------------|
G-----------------------------------------------9--11--12--(12)wf-----------|
D------------------------------------9--11--12------------------------------|
A--------------------------7--9--10-----------------------------------------|
E--14-12-12~~~~--7--9--10---------------------------------------------------|

E---------------------------------------------------------------------------|
B------------------------------------------\10---12--8--10--7--8-----7------|
G-----------------------7-6-7--(7)p6h7p6/4------------------------9-----7---|
D--9/4--4\5--5/2--2-2-2-----------------------------------------------------|
A---------------------------------------------------------------------------|
E---------------------------------------------------------------------------|

E---------------------------------------------------------------------------|
B---------------------------------------------------------------------------|
G--9--7--6------------------------------------------------------------------|
D-----------9ph~~~~---------------------------------------------------------|
A---------------------------------------------------------------------------|
E---------------------------------------------------------------------------|

repeat each position twice except for position 4
  Position 1                       Position 2
E--9-5-7-5-9-5-9-5-7-5-9-5-7-5-9-|-10-7-9-7-10-7-10-7-9-7-10-7-9-7-10-7-----|
B--------------------------------|------------------------------------------|
G--------------------------------|------------------------------------------|
D--------------------------------|------------------------------------------|
A--------------------------------|------------------------------------------|
E--------------------------------|------------------------------------------|

  Position 3                                Position 4
E-12-9-10-9-12-9-12-9-10-9-12-9-10-9-12-9-|-14-10-12-10-14-10-12-10-15-12---|
B-----------------------------------------|---------------------------------|
G-----------------------------------------|---------------------------------|
D-----------------------------------------|---------------------------------|
A-----------------------------------------|---------------------------------|
E-----------------------------------------|---------------------------------|

E-14-12-15-12-14-12-|-17--14--15------14----------17b19~~~~~----------------|
B-------------------|-------------17------15--17----------------------------|
G-------------------|-------------------------------------------------------|
D-------------------|-------------------------------------------------------|
A-------------------|-------------------------------------------------------|
E-------------------|-------------------------------------------------------|

Harmonized Part:
E---------------------------------------------------------------------------|
B---------------------------------------------------------------------------|
G--------------------------------------12--14--16--(16)wf-------------------|
D--------------------------12--14--16----------------------12/7--7\9--9/5---|
A--------------10--12--14---------------------------------------------------|
E--10--12--14---------------------------------------------------------------|

E---------------------------------------------------------------------------|
B------------------------------\10---12--8--10--7--8-----7------------------|
G-------11-9-11--(11)p9h11p9/7------------------------9-----7--9--7--6-7ph~-|
D-5-5-5---------------------------------------------------------------------|
A---------------------------------------------------------------------------|
E---------------------------------------------------------------------------|

repeat each position twice except for position 4
  Position 1                                Position 2
E-12-9-10-9-12-9-12-9-10-9-12-9-10-9-12-9-|-14-10-12-10-14-10-14-10-12-10---|
B-----------------------------------------|---------------------------------|
G-----------------------------------------|---------------------------------|
D-----------------------------------------|---------------------------------|
A-----------------------------------------|---------------------------------|
E-----------------------------------------|---------------------------------|

                      Position 3
E-14-10-12-10-14-10-|-15-12-14-12-15-12-15-12-14-12-15-12-14-12-15-12-------|
B-------------------|-------------------------------------------------------|
G-------------------|-------------------------------------------------------|
D-------------------|-------------------------------------------------------|
A-------------------|-------------------------------------------------------|
E-------------------|-------------------------------------------------------|

  Position 4
E--17-14-15-14-17-14-15-14-19-15-17-15-19-15-17-15-|-21--17--19------17-----|
B--------------------------------------------------|-------------20------19-|
G--------------------------------------------------|------------------------|
D--------------------------------------------------|------------------------|
A--------------------------------------------------|------------------------|
E--------------------------------------------------|------------------------|

E----21b22~~~~~-------------------------------------------------------------|
B-20------------------------------------------------------------------------|
G---------------------------------------------------------------------------|
D---------------------------------------------------------------------------|
A---------------------------------------------------------------------------|
E---------------------------------------------------------------------------|


Solo 3: Matt
E--7---------9---------10--------12--------10-7----7-10-7-10-7----7-10-7-10-|
B--10b12~~~~-12b14~~~~-13b15~~~~-15b17~~~~------10-------------10-----------|
G---------------------------------------------------------------------------|
D---------------------------------------------------------------------------|
A---------------------------------------------------------------------------|
E---------------------------------------------------------------------------|

E-7----7-9-7----7-9-7-9-7----7-9-7-9-7----7-10--------12--------14----------|
B---10-------10-----------10-----------10---13b15~~~~-15b17~~~~-17b19~~~~---|
G---------------------------------------------------------------------------|
D---------------------------------------------------------------------------|
A---------------------------------------------------------------------------|
E---------------------------------------------------------------------------|

E--15--------22-19----19-22-19-22-19----19-22-19-22-19----19-21-19----19-21-|
B--18b20~~~~-------22----------------22----------------22----------22-------|
G---------------------------------------------------------------------------|
D---------------------------------------------------------------------------|
A---------------------------------------------------------------------------|
E---------------------------------------------------------------------------|

E-21-19----19-21-19-21-19----19-19------------------------------------------|
B-------22----------------22----22b24~~~~-----------------------------------|
G---------------------------------------------------------------------------|
D---------------------------------------------------------------------------|
A---------------------------------------------------------------------------|
E---------------------------------------------------------------------------|

Harmonized Part:
E--10--------12--------14--------15-----------------------------------------|
B--13b15~~~~-15b17~~~~-17b19~~~~-18b20~~~~----keep-this-bend-sustained------|
G---------------------------------------------------------------------------|
D---------------------------------------------------------------------------|
A---------------------------------------------------------------------------|
E---------------------------------------------------------------------------|

E--14--------15--------17--------19-----------------------------------------|
B--17b19~~~~-18b20~~~~-20b22~~~~-22b24~~~~----keep-this-bend-sustained------|
G---------------------------------------------------------------------------|
D---------------------------------------------------------------------------|
A---------------------------------------------------------------------------|
E---------------------------------------------------------------------------|

there you go