What does this mean? Is it that you have to have a pet that's 3rd gen?  Or can you catch the 'bosses' on the island?  It is one of the requirements for a quest.

Descendant of Heroes is the same thing as Genetic Power Level (aka GPL). A topic which is already well covered by the FAQ:

What is Genetic Power? How can I get it for my pets?

Genetic Power is a bonus which child will get if the parents were properly trained before conceiving a baby.

Genetic Power gives +10 bonus to each characteristic for each Grade (in total +60 characteristics bonus for each Grade). The other profit from Genetic Power are access to temples which give you items for free if you qualify for their Genetic Power requirements, and the ability to fulfill the most high-paid quests.

The rules of acquiring Genetic Power:

If both of the parents have level 50, their child will get +1 Genetic Power.

If one of the parents is level 50 and the other is not, the child will get +1 Genetic Power if it has more dominant genes from the level 50 parent than from the parent who hasn't reached maximum level.

If both of the parents has similar grade of Genetic Power, the child will get this grade and +1 grade if one or both parents have maximum level (according to the first rule)

If parents have a difference of 1 grade of Genetic Power, the child will get the grade of the parent from which it inherited more dominant genes.

If parents has a difference of 2 or more grades of Genetic Power, the child won't get Genetic Power grade from its parenetes genes, it can get only 1 Grade for parents' levels.

Ah ok thank you :3