Each submergence will present you with lots of different fish swimming around. You will get rewards for hunting any of them, but to progress through missions and gain extra rewards you need to hunt specific targets!

There are three targets per mission, but you'll usually have to catch each target fish several times.

Each target has its own chance of appearance, which depends on your suit's rating. 

Sometimes the rating of your suit may be too low to cause a particular target to show up.  Upgrade your suit constantly to avoid that situation.