Every expository article on hyperkähler manifolds that I have read states without detailed proof the following fact: I have trouble trying to see this. Indeed, for the metric to be hyperkähler we require the holonomy group to be in (where ), so a least the holonomy should be in , which means that the Levi-Civita covariant derivation of is . This is a condition stronger than Ricci-flatness at first glance and I can't see how to realize this only knowing the existence of Ricci-flat metric.