Recent studies have reported the existence of an epitaxially-stabilized tetragonal-like (T-like) monoclinic phase in BiFeO3 thin-films with high levels of compressive strain. While their structural and ferroelectric properties are different than those of rhombohedral-like (R-like) films with lower levels of strain, little information exists on magnetic properties. Here, we report a detailed neutron scattering study of a nearly phase-pure film of T-like BiFeO3. By tracking the temperature dependence and relative intensity of several superstructure peaks in the reciprocal lattice cell, we confirm antiferromagnetism with largely G-type character and TN = 324 K, significantly below a structural phase transition at 375 K, contrary to previous reports. Evidence for a second transition, possibly a minority magnetic phase with C-type character is also reported with TN = 260 K. The co-existence of the two magnetic phases in T-like BiFeO3 and the difference in ordering temperatures between R-like and T-like systems is explained through simple Fe-O-Fe bond distance considerations.