The low- and medium-spin level structure of ⁷⁷As nucleus has been investigated using the ⁷⁶Ge(α, p2n) fusion evaporation reaction and the standard in-beam γ ray spectroscopic technique. The deexciting γ rays were detected with the Indian National Gamma Array spectrometer comprising Clover and LEPS detectors. The previously known 9/2⁺ yrast positive-parity band, based on the π(g_9/2) configuration, has been extended to the excitation energy of E_x ≈ 7.5 MeV with J^π = (33/2⁺). An extension of the high-lying negative-parity band, based on the π[(g_9/2)] ⊗ ν[(g_9/2)(f p)] configuration, has been made up to E_x ≈ 5.1 MeV, J^π = (25/2⁻). The yrast positive-parity α = −1/2 signature partner band has newly been identified and the occurrence of large signature splitting associated with the partner bands have been observed. A quasi-γ vibrational band structure built on the nonyrast 13/2⁺ state has also newly been established. The experimental findings have been interpreted on the basis of the predicted results from the total Routhian surface, particle plus triaxial-rotor model, and shell-model calculations. The band crossing phenomena correlated to the ν(g_9/2) alignment and the perseverance of triaxial shape up to the highest observed excitation regime of the 9/2⁺ yrast positive-parity band have been discussed. The evidence for the possible onset of the stapler-like mechanism prevailing in the high-lying negative-parity band structure are presented.