Wall stud would be preferred. If not a few dabs of LocTite PL3 on the back and #12 Phillips head sheet metal screws.
Hold the cabinet in place, have someone place tape on the wall at one edge and bottom and drill two holes top and bottom thru cabinet and the 1/8” thick wall panel that are the diameter of the solid portion of the screw. Now drill the same holes in the cabinet to just larger than the screws. Dab a few balls of the adhesive on the back a few inches in from the cabinet edges so adhesive does not squirt out past the edges. Place the cabinet to wall aligning side and bottom to tape so holes align. Now gently screw the fasteners just so they snug the cabinet to the wall.
With that adhesive it will never fall off the wall.