The Phase-Locked Loop (PLL) is essential for precise carrier phase tracking in Global Navigation Satellite Systems (GNSS), but it is highly susceptible to environmental interference, leading to cycle slips. This paper explores the non-linear dynamics of a second-order PLL equipped with an arctangent discriminator, with a focus on its transient response under challenging GNSS conditions, where signals undergo severe amplitude and phase scintillations. PLLs inherently exhibit nonlinearity due to the characteristics of the phase detector, a feature that is further exacerbated by the Doppler effect, which induces phase differences and tracking errors. Existing analyses often fail to fully capture the impact of these nonlinearities, presenting significant challenges in PLL design. Phase portrait analysis is utilized to visualize the PLL’s behavior, including fixed points, limit cycles, and saddle points, providing valuable insights into its stability and dynamic regimes. Key metrics such as the hold-in, pull-in, and lock-in ranges are derived, and the domain of attraction and separatrix are estimated to deepen the understanding of the PLL’s performance. This study aims to advance PLL design principles for GNSS applications, enhancing accuracy and reliability in carrier tracking and supporting precise positioning applications.