Vanquish

Only on Act 2-3: Nightmare

Remember the KNRB-0 Argus from Act 1-3 (Giant)? Well, you'll be facing two of these now! I suggest doing this one on casual difficulty, preferably using level select after having beat the game. From the start of this Act, enter the building in front of you, destroy the few enemies inside, and once you're back outside, you'll find 2 of these KNRB-0 Argus robots. One will be four-legged, the other one in the back will be two-legged. It took me a moment to figure out what I had to do, until someone put me on track (thanks kr4t0s). In order to get this achievement, both KNRB-0 Argus robots have to be two-legged before you destroy them!

Take care of the four-legged one to start with, because the two-legged one in the back won't be attacking you (unless you start attacking it) as it'll be too busy attacking the ally ship flying around (thanks Solty). Back to the four-legged one, shoot its weak spots on the arms and legs, and the core when exposed. From the moment the core gets destroyed, a QTE will be triggered.

Remember, in Act 1-3, you had to use the buttons as prompted to make the Argus transform into its second phase? In this Act, it is the opposite!! Pressing the correct buttons when prompted, is NOT what we want to do this time, because this will destroy the Argus. Instead, do nothing at all in this QTE!! It will transform into its second phase and become two-legged (bi-pedal). Destroy both of them when 2-legged.

Here's a video that might help. The author starts attacking the 2-legged one first, then the 4-legged one. In fact, it doesn't matter which one gets destroyed first. But the video should give you an idea.