His parents worked desperately hard to send him to college.
Literal
Parents [topic-は] him [object-を] university [to-に] send-intending [manner-に] desperately worked-hard.
やる here means 'to send a person somewhere' — a plain/casual form with a similar meaning to 行かせる (causative). ~ようと expresses intent or purpose: 'intending to send him.' 必死に (desperately, with all one's might) conveys the intensity of their effort.