This achievement is for defeating the last boss in the game and cannot be missed.
This is the same as the similarly named achievement from the original 360 version.
Here is the original solution from Onsidic.
Final Boss fight.
Phase 1 - Dragon Stage
Phase 1 a -
*** Spoiler - click to reveal ***Dragon will run around when his fist/paw glows orange red, he is going to try and attack you.
LB+RB to mount up and keep locked on so you know where he is at all times.
Once he charges at you Ruin Charge and circle around you should be able to slash him once. If he gets too far away you can charge at him and slash him.
Once you slash him once he will fall down on the ground.
You can attack him a few times depending on how far you were away from him when he fell, if close aim for around 10 slash if further away around 5.
Get back on your horse instantly.
Phase 1b
*** Spoiler - click to reveal ***He will fly up in the air, you wont be able to see him but he will try and dive at you and ground pound. The trick to this part is as soon as he scream/screeches the first time, Ruin Charge away.
If you can manage it circle around quickly and get a hit in on him, he will again lay down on the ground and you can repeat what happened in part 1a.
Phase 1c
*** Spoiler - click to reveal ***He will charge at you and you will be given the option of pressing B (just spam the button).
Small cutscene and will be given the option to spam B again.
Another cutscene follow and onto phase 2.
Phase 2 - Human Form.
*** Spoiler - click to reveal ***He has a number of abilities and tend to add more the further you get into this fight.
When he hold his out to his left with his left hand, just keep circling sideways (it usually better to back out as soon as you meet him in human form)
Once he has done this, dash in, hit a few times then dash out.
When you are in close he will grab the sword with his right hand and try and slash you a few times. Just dash out when he moves his right hand, and you will avoid it.
You will the get a second where you and Human Form sword fight against each other, spam X to win this part of the encounter.
After you beat him the first time, he will fly up and off to the distance.
He will then produce 3 large rocks and will throws these at you one at a time.
Keep moving to the left or right (which ever has more space to get to the edge, if your in the middle just walk either direction),
As he fires each at you, just dash to the side. then keep walking in that same direction, dash the next rock then walk in the opposite direction and repeat for last rock.
He will also have 2 new abilities.
The first is he holds his sword straight back behind him from waist level and then charges you.
This can easily be dashed to the side, given you the opportunity to get a few slashes in on him.
The second ability he uses is after you lay some slashes on him. He will fly straight up and come smashing down to the ground also producing an area effect with damage. Again quickest way is to dash backwards once or twice to be certain.
After a while you will the get another War vs Human Form sword fight against each other, spam X to win this part of the encounter.
After you beat him again, he will fly up and off to the distance and start throwing rocks, just use the same strat as earlier on in this guide.
Once he comes back he will use all the previous abilities and will sometimes quickly teleport and charging pierce you. Just simply dash out of the way.
Other ability he used rarely was he surrounds him self in an orange glow and hits you once-twice, couldn't tell what the telltale sign of this happening was. He did only use this twice.
Watch the cutscene, and earn your achievement.
Then watch the credits if you really want to.