He isn't, that is the main criticism. He usually uses actual research, yes, but then extrapolates widely and without empirical support.
For example he uses observed gender differences in the Big Five traits (which are actually there, though keep in mind the Big Five traits by themselves are already about 50% society, not genes), but then postulates differences in e.g. natural sciences, which cannot reasonably derived from this base.
His postulations often also actually stand in contrast to empirical evidence. For example in eastern Germany, the area of the former GDR, where gender equality was officially mandated and thus stronger than it is even now in Germany, girls had on average better math grades than boys in the 90s and early 2000s (see the national TIMSS data for these periods. This effect only disappeared in generations born after German reunification.
All this isn't surprising as Peterson is a Jungian (which is quack psychology), and to my knowledge has no empirical background.