You can earn this trophy after defeating the Guardian Ape for a second (third?) time.
*** Spoiler - click to reveal ***After defeating it the first time at the bottom of the Sunken Valley, he appears again right after the poison pool section of the Ashina Depths.
This new fight is pretty annoying as you have to basically fight both of his original phases at the same time, as a new Ape joins the fun.
The easiest way to take care of the normal ape is to use an upgraded Flame Barrel and try to apply the burn status with the big flame blast. This will stun it for a long while and deal a bunch of damage. Be patient and look for openings to use the tool and if you can get a successful hit each time, that should take care of the second ape all by itself. After the normal ape is dealt with, the guardian ape is the same as phase two of the first fight.
As is teased after first defeating the Guardian Ape,
After defeating him, approach the corpse and there will be a second deathblow indicator where you can use the Mortal Blade to finish it off.
If you happen to defeat this boss before acquiring the Mortal Blade, the trophy will be missed and you'll have to wait until NG+, so don't go here without the Mortal Blade!