When I heard the news of my father's sudden death, I was completely overwhelmed.
Literal
Father's sudden-death's news [object-を] hearing, I [topic-は] composure [subject-が] overturned-completely.
急死 = 'sudden death.' 気が転倒する means 'to lose one's composure / to be thrown into confusion.' てしまった adds the nuance of an uncontrollable, regrettable outcome.