He is guaranteed victory in
8 moves. There are 8 possible scenarios, with shot totals of 5, 6, 6, 7, 6, 7, 7, 8. They are all described below.
Since the carrier has not yet been hit, we know that it must be in one of the spaces that are at least 5 squares long.
His first shot $S_1$ is:
E4
This overlaps with a carrier sitting vertically somewhere in the range A4-I4 or horizontally somewhere in the range E1-E8.
If it's a hit, his second shot $S_{2,1}$ is:
E5
A hit on E5 means that the carrier is positioned horizontally. His next shots extend to the right starting with E6.
If his next three shots all hit, he has sunk the carrier using 5 shots.
If one of his shots to the right misses, he begins shooting left starting with E3. The carrier will have been sunk using 6 shots.
If $S_{2,1}$ is a miss, his third shot $S_{3,1}$ is:
D4 and then continuing up the grid.
A miss on E5 means the carrier is vertical.
If these four vertical shots all hit, the carrier has been sunk using 6 shots.
If one of the shots misses, he fires at F4 and continues downwards until the carrier is sunk in a total of 7 shots.
In the event that $S_1$ misses, his second shot $S_{2,2}$ will be:
B4
In the event of a hit, we know the carrier is horizontal. If it were vertical, $S_1$ would have also hit the carrier. 4 more shots to the right will sink the carrier in 6 shots.
If the final shot misses, one shot fired at B3 sinks the carrier bringing our total to 7 shots.
In the event that $S_{2,2}$ also misses, his third shot $S_{3,2}$ will be guaranteed to hit at:
H4
Here, we might be hitting a vertical carrier (F4-J4) or a horizontal carrier (H4-H8).
Testing H5 $S_4$ will determine the orientation.
If $S_4$ is a hit, three more shots at H5-H8 will sink the carrier in a total of 7 shots.
If $S_4$ is a miss, we know the carrier is positioned vertically. The carrier will be sunk by the remaining shots F4, G4, I4, J4; a total of 8 shots.