During act 14 you will be given the option to choose yes or no, choose no and complete the rest of the mission. If you choose yes you will not get this trophy.
*** Spoiler - click to reveal ***Once you choose no you will have to fight another robot dog and a timer will start. After you kill him keep progressing until you come into a room where you have to fight some saber tooth tigers, then two raptors.
Once you defeat them you will have to fight the final boss, which is another robot dog. He has three moves, a dash attack, energy balls, and a rotating laser beam mixed in with some energy balls. There are two platforms off to the left of the screen where you can go to avoid the laser and energy balls.
Once you defeat him just keep progressing until you get the final cutscene.