What are all of the greek heroes, their parent that is a god, and the monsters they killed. Also their relation to any one important.
You might be shooting for quite a bit here. I would propose a bit more clarification offered. If I understand correctly, you are analyzing the history of Greek Mythology Heroes, any potential shared lineage and the similarities in their deeds of killing adversaries. In order to do this, I would clearly identify two heroes of Mythology. A good example would be Perseus and Theseus. At this point, I would find out who the heroes' birth-parents were, and if there was an Olympian God involved. I would also examine some of their similarities in how they were brought up and anything unusual that might have been present at their birth. For example, is there a prophecy or some type of oracle which presents itself at their birth or throughout their childhood. Finally, in analyzing their deeds, I would try to examine if there is any similarity in the adversaries they defeated and how they were able to do so.
It is flat out impossible to name all the Greek heroes. There are too many and more importantly, their lineages differ greatly. If you read the ancient sources, sources will differ (sometimes a lot). So, let me give you a few to get you started. For a more extensive list, I suggest you take a look at Timothy Gantz's two volume on Greek mythology. This book will get you started and keep you busy for a long time. One of the most famous heroes in Greek mythology of Heracles. Heracles was the son of Zeus and Alceme and he killed plenty of monsters, like the Nemean lion and the Cretan bull. Another famous hero is Theseus, who according to some was the son of Poseidon.