Defeat Achilles with the pre-selected spear by dodging to his side or back when he charges Jason and thrusting out once with the Lethal blow. If the hit spark is gold or yellow, the hit will be a dud, but occasionally you will score a bloody injury. A second method is to block Achilles as he's incoming and then counter-attack twice with Wounding (weaker) blows. This process is just as long as the first; the champion of Hellas doesn't drop dead easily.
Defeating Pelias
Defeat Pelias by throwing Jason's spear towards him (at first) after he's exhausted his magic beam against Jason's shield (block the beam's whole duration). When Pelias changes his attack pattern and shoots magic missiles from the air, power block (guard and press the shield shove button) to reflect the missiles back at him. When Pelias changes his attack pattern a final time and shoots magic missiles from the ground, simply dodge his attacks and rush him with melee weapons. Destroy his shield with melee attacks and fertilize his the ground with his fetid corpse.
Invincibility
Note: always make backups! Use a text editor to edit the "LiquidGame.ini" file (in the \My Documents\My Games\Rise of Argonauts\Liquid Game\Config directory in XP).
Change the value of the MediumDifficultyDamageModifier line (or the line that corresponds to whatever difficulty you are playing) from 1.0 to 0.0. Save and start the game and you will be invincible.
Unlimited Dialogue
After receiving Hermes's Sight on Saria, go to Callas (outside the cave. Talk to Callas, then return to Agrios (in the village). You'll be asked to match three choices in order to convince him to take down the body. Pick a different god's response after the first dialogue choice (e.g. choose Hermes and pick Ares's option "He belongs in Tartarus") and Agrios will refuse to take the body down -- and that's just what you want him to do. Continue to make the wrong choices and you'll build dialogue choices for all the gods. These options satisfy the gods' dialogue quotas. This is an easy way to get Apollo's 75 choice deed.