In this work we firstly study the influence of different parameters in the temporal characterization of ultrashort laser pulses with the recently developed amplitude swing technique. In this technique, the relative amplitude of two delayed replicas is varied while measuring their second-harmonic spectra. Here we study the retrieval of noisy traces and the implications of having different delays or phase retardations (relative phases) between the two replicas. Then, we study the capability of the technique to characterize the pulses when the second-harmonic signal is spectrally uncalibrated or incomplete, presenting the analytical calculation of the marginal, which is used to calibrate the traces and to perform the pulse retrievals. We experimentally show the retrieval of different pulses using diverse delays and phase retardations to perform the amplitude swing trace and demonstrate that, from an uncalibrated trace, both the pulse information and the response of the nonlinear process can be simultaneously retrieved. In sum, the amplitude swing technique is shown to be very robust against experimental constraints and limitations, showing a high degree of soundness.