Hydraulic jumps are widely used to dissipate excess energy in civil, ocean, and hydro-power engineering, particularly in high dams with large reservoirs. Different inflow and tailwater conditions lead to the occurrence of various types of hydraulic jumps. Among them, A-jumps are often preferred for stilling basin design, due to their high energy dissipation efficiency and favorable outflow patterns. This study numerically investigated the hydraulic characteristics of 75 critical A-jumps by adjusting tailwater levels, considering varying inflow conditions (flow depth, velocity, discharge, and Froude number) and stilling basin parameters (negative step height and incident angle), covering key parameter ranges from existing practical applications in high dam projects. Based on theoretical analysis and numerical simulations, estimation methods are proposed for the key hydraulic parameters of A-jumps, including the sequent depth ratio, roller length, reattachment length, and energy dissipation rate. A correction for the sequent depth ratio, incorporating the influence of the incident angle, is proposed for the first time. These estimation methods offer valuable insights for designing and optimizing negative step stilling basins in various practical engineering scenarios. To validate their applicability, a case study was conducted, showcasing the superior energy dissipation and stable outflow performance of the designed stilling basin, with the basin length shortened by 1.8% and the near-bottom velocity reduced by 42.4%, based on the proposed estimations, compared to the classical stilling basin.