Flapping-wing micro air vehicles (FWMAVs) have demonstrated remarkable bio-inspired agility, yet tailless two-winged configurations remain largely unexplored due to their complex fluid-structure and wing-body coupling. Here we present \textit{AirPulse}, a 26-gram butterfly-inspired FWMAV that achieves fully onboard, closed-loop, untethered flight without auxiliary control surfaces. The AirPulse robot replicates key biomechanical traits of butterfly flight, including low wing aspect ratio, compliant carbon-fiber-reinforced wings, and low-frequency, high-amplitude flapping that induces cyclic variations in the center of gravity and moment of inertia, producing characteristic body undulation. We establish a quantitative mapping between flapping modulation parameters and force-torque generation, and introduce the Stroke Timing Asymmetry Rhythm (STAR) generator, enabling smooth, stable, and linearly parameterized wingstroke asymmetry for flapping control. Integrating these with an attitude controller, the AirPulse robot maintains pitch and yaw stability despite strong oscillatory dynamics. Free-flight experiments demonstrate stable climbing and turning maneuvers via either angle offset or stroke timing modulation, marking the first onboard controlled flight of the lightest two-winged, tailless butterfly-inspired FWMAV reported in peer-reviewed literature. This work corroborates a foundational platform for lightweight, collision-proof FWMAVs, bridging biological inspiration with practical aerial robotics. Their non-invasive maneuverability is ideally suited for real-world applications, such as confined-space inspection and ecological monitoring, inaccessible to traditional drones, while their biomechanical fidelity provides a physical model to decode the principles underlying the erratic yet efficient flight of real butterflies.