I also find difficult to define the subproblems so any hint would help.
I thought of each subproblem is the max amount of gold she can get by shooting the 1st enemy, then the second, etc and on each enemy there are four possibilities:
a) shoot the enemy and kill him
b) shoot the enemy without killing him
c) don't shoot, which means the tower will shoot and the enemy might be killed or not
d) don't shoot, which means the tower will shoot but it doesn't kill him.
But I don't know how to proceed from this, and if it's a good way to think about the problem..