When an ionic conductor meets an electronic conductor, ions and electrons couple at the interface between ionic and electronic circuits, enabling a class of devices: ionotronics. Such a coupling gives innovations but can cause electrochemical breakdown. Rapid advances in hydrogel ionotronics, in which hydrogel serves as stretchable, transparent, ionic conductor, highlight an urgent need: a general approach and criterion to study electrochemical breakdown under AC condition. Here we study the breakdown behavior of a metal-hydrogel-metal ionotronic system subject to alternating voltages of various frequencies and amplitudes. First, we apply a sinusoidal voltage to the ionotronic system which is connected in series to a load resistor, and compare the waveforms of the applied voltage and the output voltage between the two ends of the load resistor at various frequencies and amplitudes. Electrochemical breakdown tends to take place at low frequencies and high amplitudes, and causes distortion of waveform of the output voltage. Next, we develop an electric circuit model, in which each hydrogel-metal junction is modeled as a constant phase element in parallel with a leakage resistor and the hydrogel is modeled as a resistor. Our experiments show that the electrochemical window is insensitive to the frequency and amplitude of applied voltage, as well as to the concentration of ions in the hydrogel. Through a combination of experiment and theory, we further propose a frequency-amplitude phase diagram. Different from DC condition, the breakdown behavior under AC condition depends not only on the amplitude of applied voltage, but also on the frequency of applied voltage. We also show that electrochemical reaction can be retarded by stretching the hydrogel and by increasing the frequency. It is hoped that this work will guide the development of stable and reliable hydrogel ionotronic devices.