Well, I'll do my best =/
Jason - Leader of "The Argonauts" a quest to get the golden fleece, which thanks to medea (sorceress daughter of the king where the golden fleece was) was succesful. To get the fleece he had to yoke 2 bulls who breathed fire and use them to plow a field and plant dragons teeth which caused armed warriors to spring up and attack, thanks to medeas magic he was succesful.
Odysseus - Hero of the odyssey basically after the Trojan War Poseidon was angry with him and caused him to wander facing many dangers such as scylla and some others before he could finally return home to his family.
Heracles - Son of Zeus did lots of great things and of course the famous 12 labors. (most people know him as Hercules :/)
Bellepheron - Was tasked to kill the Chimera, something which was meant to kill him, but thanks to blessings from the gods he got the Golden Bridle of Pegasus thus letting him kill the Chimera, but he lost the help of the gods and became a beggar when he attempted to fly to Olympus.
Ajax - Fought for the Greeks in the Trojan War, when he did not get the Armor of Achilles he planned to kill all of his armies leaders, but Athena caused him to slaugher pigs and cows instead, upon seeing what he had done he killed himself.
Chiron - One of the few 'civil' centaurs. He trained/taught many of the greek heroes
Achilles - Warrior of the greeks who was invulnerable except in his famous heel, where he was shot by a poisoned arrow from Paris (guided by apollo) causing his death.
Perseus - Slayer of the Gorgon, also saved a maiden from a sea monster by killing it.
Theseus - Another Greek who looked up to Hercules, he traveled the land and killed many minor villians before deciding to kill the Minotaur, he succeeded but told his father that if he was succesful he would fly white sails on his return, he forgot and sailed black causing his father to kill himself.
Hippolyta - Was a queen of the Amazons who was killed by Hercules during one of his labors.
Atalanta - A powerful female warrior and hunter who was raised by bears, she was told by the oracle never to marry, but eventually did so due to losing a foot race when her opponent threw Golden apples in her path distracting her, After marrying she and her husband were eventually turned into a Pair of Golden Lions.
Polyphemus - A cyclops who met odysseus, and was blinded by him, appears in some other stories where he falls in love with a nymph.
As far as I know most of thats correct, if anyone wants to correct, or add, feel free