High power-density power electronics are needed for a wide range of applications, such as renewable energy, transportation, and telecommunication and computing. This work demonstrates a high-performance totem-pole flying capacitor multilevel converter utilizing gallium-nitride switches, capable of greatly increased power density compared to conventional designs. Challenges surrounding the control and operation of the totem-pole bi-directional ac-dc converter are detailed, and showcase that this complex topology can be translated into a highly power-dense prototype. An ac voltage of 240 Vrms at 60 Hz is converted to a dc voltage of 350 V - 400 V. The converter is designed to achieve a power density of > 2000W/in3, and a peak efficiency of 98.8% through high-performance layout and design techniques.