This study explores the hydrodynamic performance of a National Advisory Committee for Aeronautics 0012 foil using computational fluid dynamics with the unsteady Reynolds-averaged Navier–Stokes (URANS) method and shear stress transport k-ω model to assess the impact of asymmetric motion parameters in manta-like swimming. The angles of attack during the mid-upstroke (αmu), mid-downstroke (αmd), and stroke duration (S) are varied to understand their effect. At low Strouhal numbers (StA = 0.2–0.35), a smaller αmd compensates for thrust loss at the start of the upstroke due to a greater αmu. At high Strouhal numbers (StA = 0.5), a greater αmd reduces negative thrust and compensates for the smaller thrust generated by a small αmu during the upstroke. Shorter stroke durations increase asymmetry, leading to more significant positive thrust peaks during the downstroke. If both the angle of attack and S are large, the slower downward speed extends negative thrust, reducing thrust peaks and lowering average thrust. A smaller stroke duration combined with a large angle of attack enhances efficiency due to a greater thrust-to-power ratio, highlighting the interplay between these parameters. A smaller S and greater αmd and StA maximize thrust and efficiency, suggesting aquatic organisms increase thrust while ensuring propulsion efficiency by using a large angle of attack and an asymmetric stroke duration. This study demonstrates how asymmetric parameters interact, providing insights into designing biomimetic underwater vehicles. The findings suggest that asymmetric dynamics enhance propulsion efficiency.