Kill 1000 UFOsThis is cumulative across both Challenge and Arcade mode. You'll be going up against far more Asteroids than UFOs, so there's a chance this will be one of the last trophies you earn. As soon as you've killed your 1,000th UFO, the trophy will unlock.
If you want to grind this out instead of waiting for it to unlock naturally, you can replay Challenge #28, "Dominant Strategy", repeatedly until you get it. This Challenge requires you to kill 60 Asteroids, but all of the Asteroids will have a UFO stuck in them, giving you a minimum of 60 UFOs per run. If you grind this out last/after you completed Challenge Mode and earned 6,000 points in Arcade for The Invisible Man , you shouldn't have to spend too much time grinding it out.