On the first level you will engage in a big fight with a Hydra twice, the second time you encounter him there are 3 heads you need to kill, 2 at the bottom which if you do not kill first you will be pulled back to the ground. So basically you need to kill them first.
Just keep going between the 2 of them and you can use your new special power you was just granted on them which helps speed things up. To use it press right on the D-pad and hit R1.
After attacking for a while the head will hit the deck and allow you time to climb a set of boxes to either side of which ever head you are attacking. Left head, boxes to the left, Right head boxes to the right. Double jump until you are at the top and you should be prompted to start a quick timed event to finish the head off.
Once you have done that for both you can finally climb the ships netting to the main head of the Hydra, my biggest tip is to hold block (L1) when it starts to try blow you back to the bottom deck because if he does his life regenerates, between those attacks just use the roll button (Right Analogue Stick) out of the way when he is going to snap at you, here is where you get your chance to use the special attack i spoke of earlier, once he snaps and is close enough with his head right next to you otherwise just keep hitting him with fast then heavy attacks and sometimes you get green and blue orbs recharging your own health and special attack energy. Once he is down and O comes up on the screen prompting you to do more quick time events do so then repeat the normal attacks again keeping in mind to block (L1) if you think he is about to try blow you back down to the lower deck. Three QTEs and he will be dead and you hear a voice shouting for help, head in to the mouth of the large head then collect the key.
Once you have collected it the trophy pops. It is story driven but i thought a few tips wouldn't hurt.