After completing the game, you can easily unlock any of the "X kills with X weapon" trophies using the following method.
First, from the main menu go to Bonuses/Store/Weapons and purchase the M4 assault rifle. Now go to Bonuses/Store/Tweaks and purchase Infinite Ammo.
Use Chapter Select to load up Chapter 4 - The Dig, and set the difficulty to Very Easy. Make your way a short ways into the chapter until you get to the shed where you receive the grenade tutorial, then hit pause and use the menus to select the M4 and "Give Weapon", then use them again to "Enable" Infinite Ammo. After the cutscene and the tutorial, the bad guys will start coming. Now just go to town killing the 20-25 enemies that spawn in this area. When Sully get surrounded up on the high ground, hit pause and Reload Checkpoint to start back at the beginning. You will have to go into the menus to re-equip your M4 each time, but meh. Rinse and repeat until you get your 70 kills and your trophy.
Note: The trophy will unlock as soon as you get the 70th kill.