What is refer to the mischance of the hour? How could they save themselves from the mischance?

The mischance of the hour refers to the possibility that the ship might sink in the storm. The Boatswain says the king's advisor might council the wind and the sea to stop battering their ship. He is of course being facetious.

How could the people on the boat save themselves from the mischance of the hour?

by praying to god and getting inside the cabin

Mischance of the hour refers to the possibility of the ship to sink in the fierce storm. People aboard the ship could save themselves by staying inside their cabbins calmly and not disturbing boatswain and other mariners. Boatswain requests all the royal lords including the king Alonso, his brother Sebastian , Ferdinand , Antonio and Gonzalo to remain inside there cabbins and not assist the storm againt them.