Block the beam he shoots at you until it ends, then shoot him with your spear. When Pelias flies around and shoots purple balls at you, hold Block. When the balls circle you press Power Block. When Pelias shoots the purple balls while he is standing on the ground, get close to him and repeatedly tap Power Block.
Defeat Achilles with the pre-selected spear by evading 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 you will sometimes 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.
After receiving Hermes's Sight on Saria, go to Callas (outside the cave). Talk to Callas, and then return to Agrios (in the village). You will 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, and Agrios will refuse to take the body down. Continue to make the wrong choices and you'll build dialogue choices for all the gods. These options satisfy the gods' dialogue quotas. By doing this you will easily be able to get Apollo's 75 choice deed.
"Children Are Annoying" hint:
The party will meet an orphan named Bolo on the island of Mycenae. Simply endure his singing by not selecting the choice ' Enough!' enough times.