Visa on arrival to see my father who is in critical condition

You need a proof of your father's condition from the hospital in Beijing, such as official notice of critical illness by the hospital.

The process is very simple, considering your emergency. You may just fill the visa application form, provide your valid passport, and pay the fee. I'm not sure whether the return air ticket is required or not now. You may get a final answer from your air company, I think.