You can see the diagram for each move by following along at this HexWorld link.
1.
a3
2.
...
swap
3.
j9
4.
...
i5
5.
k3
6.
...
j11
7.
l11
8.
...
k12
9.
f8
10.
...
d10
11.
c11
12.
...
f6
followed by (g6) h4 (g5) g4 (e5) and f3 blocks red form the top
13.
i6
14.
...
j5
15.
k6
16.
...
l4
17.
h5
18.
...
f9
followed by (g8) g9 (h8) h9 (i9) i8 (j7) j8 (l7) - blue wins [still, blue is making a lot of double threats here, so red may answer with double defences] or f9 [I believe that d10 is currently connected to the left via f6/c1 2/3rd line ladder escape...] (g8 -as this is what red must do if blue started by pushing at h6) g9...
19.
g8
g8: The trick, for red, is to play around d7 before forcing blue to connect to f6 or d10. Is there a move which threatens both which I cannot answer to save both?
g8 (e7) f7 (e8) e6 (d7) d6 (c7) d2 (g7) f9 (c10) - blue loses ;
g8 [(g7) f9?] (h7 - guards against both h6 and i7) h8 (k7) i10 (i9, red h9 answered by blue i8) h10 (h9) g10 (g9) e11 ;
g8 (h10) h6 (g6) f9 - looking good for blue
g8 (h10) h6 (