  We prove that the pure part of the cohomology ring of the moduli space of
irregular $\underline{\xi}$-parabolic Higgs bundles is generated by the
K\"{u}nneth components of the Chern classes of a universal bundle and the Chern
classes of the successive quotients of a universal flag of subbundles. As an
application, in the regular full-flag case, we demonstrate a similar result for
the cohomology ring of the moduli spaces of parabolic and strongly parabolic
Higgs bundles.
