Extracorporeal boiling histotripsy (BH), a noninvasive method for mechanical tissue disintegration, is getting closer to clinical applications. However, the motion of the targeted organs, mostly resulting from the respiratory motion, reduces the efficiency of the treatment. Here, a practical and affordable unidirectional respiratory motion compensation method for BH is proposed and evaluated in ex vivo tissues. The BH transducer is fixed on a robotic arm following the motion of the skin, which is tracked using an inline ultrasound imaging probe. In order to compensate for system lags and obtain a more accurate compensation, an autoregressive motion prediction model is implemented. BH pulse gating is also implemented to ensure targeting accuracy. The system is then evaluated with ex vivo BH treatments of tissue samples undergoing motion simulating breathing with the movement of amplitudes between 5 and 10 mm, the frequency between 16 and 18 breaths/min, and a maximum speed of 14.2 mm/s. Results show a reduction of at least 89% of the value of the targeting error during treatment while only increasing the treatment time by no more than 1%. The lesions obtained by treating with the motion compensation were close in size and affected area to the no-motion case, whereas lesions obtained without the compensation were often incomplete and had larger affected areas. This approach to motion compensation could benefit extracorporeal BH and other histotripsy methods in clinical translation.