Background: In the "island of inversion,"ground states of neutron-rich sd-shell nuclei exhibit strong admixtures of intruder configurations from the fp shell. The nucleus Mg30, located at the boundary of the island of inversion, serves as a cornerstone to track the structural evolution as one approaches this region. Purpose: Spin-parity assignments for excited states in Mg30, especially negative-parity levels, have yet to be established. In the present work, the nuclear structure of Mg30 was investigated by in-beam γ-ray spectroscopy mainly focusing on firm spin-parity determinations. Method: High-intensity rare-isotope beams of Mg31, Mg32, Si34, and P35 bombarded a Be target to induce nucleon removal reactions populating states in Mg30. γ rays were detected by the state-of-the-art γ-ray tracking array GRETINA. For the direct one-neutron removal reaction, final-state exclusive cross sections and parallel momentum distributions were deduced. Multinucleon removal reactions from different projectiles were exploited to gain complementary information. Results: With the aid of the parallel momentum distributions, an updated level scheme with revised spin-parity assignments was constructed. Spectroscopic factors associated with each state were also deduced. Conclusions: Results were confronted with large-scale shell-model calculations using two different effective interactions, showing excellent agreement with the present level scheme. However, a marked difference in the spectroscopic factors indicates that the full delineation of the transition into the island of inversion remains a challenge for theoretical models.