Make a cable with a female 3 pin header for the PIR sensor, and wire the other end to GND, VCC, and a digital I/O pin on the protoshield. It is easiest to do this using a male 3 pin header, crossing over two of the wires to put the output pin on one of the outside pins, and connecting to the GND/VCC bus down the middle.

Hook up the relay on the protoshield to switch the power from a 9V wall wart (not the one being used to power the Arduino). Do not connect the switched grounds, or the 9V sides; this should be a completely isolated circuit. Put a diode in parallel with the coil pins to dissipate the flyback current. Run the relay input pin to an I/O pin.

Run the switched power and ground through long wires to the printed battery case. Insert each of the stripped ends through one of the pairs of two holes, bend it around and insert it back through the other hole to form loops that will contact the power conductors inside the Hydrostorm. Stuff the battery case with some paper towels to soak up any water, and to help keep the contacts in place.

Mount the PIR sensor on its printed mount and attach it to the wall in with double sided mounting tape. Prop up the Super Soaker with the printed prop to an appropriate angle.

Run the sketch and wait for unsuspecting cat to come along.