Having 30 'Uncommon Fish' in your reef will help out with this one! Check your Aquapedia to see which fish are 'uncommon' - it will say this under the yellow star on each species page.
You will need to hatch 30 uncommon fish into your reef - But you need to keep them all swimming in there until you reach 30. it will keep a track on your current numbers and how many you have to go under the missions icon.
Once the mission is completed you are free to release the 'Uncommon' fish and move onto different rarities!