We demonstrate the acousto-optic modulation of a hybrid-lattice hollow core fiber (HL-HCF) for the first time. For many years, optical fibers with reduced diameters have been the main solution to increase the interaction of acoustic and optical waves. However, the high drive voltages and large modulator components still employed drastically affect the efficiency and miniaturization of these devices. Here, we experimentally show that combining Kagomé and tubular lattices in HL-HCFs allows for enhancing the amplification of the acoustic waves and the modulation of the guided optical modes, thus providing high modulation efficiency even when using a fiber with a 240 µm diameter. To the best of our knowledge, the measured HL-HCF's modulation efficiency (1.3 dB/V) is the highest compared to devices employing reduced diameter fibers. Additionally, we demonstrate a compact acousto-optic modulator with driver dimensions smaller than the HL-HCF diameter. Overall, our results show a promising alternative to solve the compromise of speed, efficiency, and compactness for integration with microscale all-fiber photonic devices.