Vanquish

Only on Act 3-2: Attack

Remember those little Pangloss statues you've been shooting at? Or perhaps you haven't found any yet? Anyways, there's a big stone one on the plaza near the end of Act 3-2. In order to get this achievement, you have to destroy every enemy and complete the mission with the big Pangloss statue intact. It is not as hard as it sounds.

When you cross the bridge and arrive at the plaza, you will be ambushed from all sides mainly by red regular robots. They aren't any threat to that statue. The real threat will be an enemy vehicle with circular saw blades in front of it, the same one from Act 1-5 (Trust). Once you've destroyed some robots, you'll get an animation of this vehicle breaking through the rubble.

This vehicle is pretty fast and can destroy the statue in a matter of seconds. So, as soon as this vehicle appears, stun it by throwing an EMP Emitter at it, then shoot at the core at the back side of it. Rinse and repeat if necessary. On casual difficulty, you can destroy this vehicle with the rocket launcher. It should take no more than 3 hits. (thanks Solty)