This trophy is pretty straightforward and very easy to do at any point in the story.
But incase you're having difficulty racking up melee kills on enemies wielding weapons, then the chapter I got it on was chapter 3, Twin Falls. Idaho. As you make your way through this mission, mostly every enemy you come across during the first half of this chapter will be ones that pop out of egg like things and run at you, trying to melee you, making it easy for you to melee them, due to it being a 1hit and them not damaging you with any form of weapon.
You are able to get hurt by them, but not too much if you're careful, there's also a point in this mission where you're swarmed by 10-20 of them at once, which you can use the grenade launcher on your carbine for, aiming for the 150kills trophy.