Spoiler (click to reveal)
Usually it is easy to completely fill up the remaining squares, however, sometimes it can be quite tricky to use them to the maximum extent possible. White controls four areas (left upper corner, left side, center, right lower side), Black three areas (upper right corner extending to both sides, lower right corner, lower left side).
Black has one tempi more than White and thus wins after 29 plies, although he has to move first. The tricky part of the puzzle is the upper right corner.
Black should play very careful and move his upper right Amazon and shoot her arrows as follows:
h9-j7/j5; j7-i8/j9; i8-j7/j6; j7-i8/j7; i8-h9/i8; h9-g9/h9;
g9-f10/g9; f10-e9/f10; e9-d9/e9