This paper examines how individuals track targets that move in relatively unpredictable trajectories. Gaze and behavioural data were captured as twenty two participants learned a simulated competitive marksmanship task known colloquially as the Death Star over six training days. Participants spontaneously selected one of two consistent target-tracking strategies with approximately equal probability. Participants employed either chasing behaviour, in which gaze follows a target's trajectory before a shot, or ambushing behaviour, wherein gaze anticipates the trajectory and the participant intercepts a moving target predictively. All participants improved in task performance measures (completion time and number of shots), but did so at the expense of accuracy in missed shot attempts. Surprisingly, neither behavioural strategy offered a significant advantage in task performance measures, indicating that either may be equally effective in tackling a hand-eye coordination task with complex target motion such as the Death Star.