There is some controversy about how useful the Hunting Instinct is, but there is one certain thing. It is completely useless if you don't know how to use it.
The Hunting Instinct can be an award from the Advent Calendar or from the Casino. You can also buy it from the overview map, or from any area.
If you click on the icon above, you will be prompted to buy. The Hunting Instinct costs 19 diamonds for an hour.
After buying it, the Hunting Instinct icon is replaced with two different icons. The Pink Hunting Instinct searches for the mission with the best experience reward per energy used.
The Green Hunting Instinct Icon finds the mission with the best notes reward per energy used. The energy reward takes the sell cost of items into account when calculating the value of a mission.
Note that the hunting instinct does NOT take into account the incredible value of a party ticket. If you have not gotten your party ticket for the day, you should always use the green hunting instinct icon from the overview map. That will let you scan for a party ticket so you do not miss it.
Select the icon for the mission type you prefer, and you will be transported to the appropriate area, with the confirmation message to accept the mission already on screen. Simply click OK to accept the mission!
Hope this helps!