The relation between universal and particular is considered to be the Achilles' heel of universal realism. However, modern universal realism with facts does not have the difficulties which traditional Platonic universal realism had. Its exemplification relation connecting particulars and universals in atomic facts is very different from Platonic participation. Bradley's regress argument against the exemplification relation can be refuted in two different ways. Nevertheless, there are good reasons to avoid the assumption of an exemplification relation and thus to go without the Achilles' heel altogether.