Well, there are a few clues here. Based on the supplied data, the system normally puts out 25 pulses per second with an amplitude of 300 volts into a 500 ohm load. They say the maximum average power is 25 watts. Using the formula: average power = peak power x duty cycle, the pulses must be about 5ms long.
So, how would you build such a circuit? Here is one idea. Buy a 50 watt 12v to 120vac modified sine wave inverter. These will put out a 60Hz waveform with 160 volt peaks. Take that output and connect it to a voltage doubler circuit, which can source about 25 watts of power. This will yield about 300+ volts DC. Next, build a 5ms pulse generator circuit, with a variable 20Hz to 50Hz pulse rate. One or two 555 timers would work. Feed the output of that to a high voltage n-channel FET (IRF744) which is connected to the electrodes. Use a 40 watt incandescent light bulb as a current limiting device in series with the FET. You could tap into the 120vac signal to power the pulser circuit. It would not need much power, perhaps 12v at 3ma. Keep in mind that this circuit is dangerous. There are some high voltages involved.