There are four summons in the game which can instantly wipe out enemies. They can't be used against bosses but they can be used in mini-bosses. You can only use them once a day. The game technically spans in three days so that means they only have a very limited number of uses. A day ends with the quests The Bard and Attack the School.
You can unlock the summons by completing certain sidequests. It is recommended to finish them as early as possible to maximize the number of uses. (you can immediately get three summons on your first day)
Here are the list:
Complete Find Jesus.
Complete Mongolian Beef
Complete Mr. Slave's Package
Complete Dropping the Kids Off