here is where the good old subquery works, and is very simple
UPDATE UserAssesment set AssessmentDate = (select top 1 comp.AssessmentDate from vw_CompletedAssessments comp where ua.NatId = comp.NatId and ua.FamilyName = comp.ClientLastName and ua.GivenName = comp.ClientFirstName order by comp.date desc ) WHERE ua.HasCompletedAssessment <> 0