"There are 12 Olympian gods. The big three are the brothers Zeus, Poseidon and Hades. They attained power by overthrowing their father Kronos, chopping him into little pieces. the three gods have been rivals ever since, always arguing always threatening war."
this statement is all correct although it is a summerised version

"The children of these unions were half god, half human. Demigod. Many became great heroes like Hercules and Achillis and Perseus."

Part of the dual nature of Greek heroes that gave rise to the modern "Demigod" a repeated theme in the story of their birth—is a double paternity: one parent is a regular mortal, and another is a God. Thus the heroes have liminal qualities that enable them to have great strength, to cross the threshold between the worlds of the living and the dead yet return safely, and to mediate long after their death between human and divine.

"Hercules and Achillis and Perseus."
this statement is also true Hercules, Achillis and Perseus were all famous demigods.

http://homepage.mac.com/cparada/GML/Achilles.html
http://www.ballpoint.org/greekgods/perseus.htm
http://library.thinkquest.org/5830/DemiGods.htm