*As far as i can tell you cannot win the first encounter.*
This is a story related trophy and cannot be missed. Charon is a boss fight and is the Ferryman of Underworld. Charon is fought twice throughout the game. You'll obtain this trophy on the second encounter and not the first encounter. Below are the phases of how to defeat him:
Boss Fight - Charon's attacks:
Scythe Combo: A standard multiple attack with his scythe.
Energy Ball: Fires 3 green balls of energy towards you.
Pyre Wall: A huge pyre wall flies at you (Instant kill).
Charon's Wraith: Breathes his specialty of Charon's Wraith (breath) on you dealing multiple hits.
Scythe Explosion: Hit's the ground with his scythe creating a green energy explosion within a blast radius.
This is the same phase during your first encounter you had against him. Just simply keep attacking him with whatever weapon of choice you choose, until his health is about 30% depleted. Eventually he’ll go on top of the ship, but this time you can attack and destroy one of the three pillars below him. Destroy a pillar and he'll come back down to face you again.
During this phase, he will start to spam you with his Charon's Wrath attack. If you get hit by his Charon's Wrath attack, he'll continuously attack you for about 5 seconds over and over again. Simply dodge or roll over these when they appear. Continue to attack him and reflect whatever he shoots at you and keep blocking his scythe attacks until he goes back onto the ship's upper area. Once again, destroy another pillar for him to come back down to face you.
During this phase, he will begin to use his Scythe Explosion attacks against you. Simply jump over these each time he performs this move and continue to attack him. You'll also notice that he becomes vulnerable to more attacking punishment when he performs a much bigger Scythe Explosion attack at the middle of the ship, due to his scythe getting stuck in the ground. After damaging him enough times you'll impale him to the ship's wall with his own scythe.
This is the final phase of the battle. Once you impaled him to the wall. Grab his mask and Charon will free himself from the wall and will now start to float around the ship. Reflect every Energy Ball he shoots at you and once he goes down, quickly run up to him and engage in the mini game by pressing the Circle Button button and complete the sequences that appears on screen until you killed Charon for good.
This solution is not my own and was taken from Playstationtrophies.org All credit goes to original author. http://www.playstationtrophies.org/game/god-of-war-chains-of...