Keyword here is "hit". You don't have to take it down, just touch it with the laser guided rocket.
It's easier said than done because that pesky chopper doesn't like to stand still and actually maneuvering the rocket can be a pain in the ass as well.
There are two places that are best suited to get it, but I found this one the easiest. Right near the end of Ghost Town, a chopper will appear. Earlier on in the mission, you will get the laser guidance system, so make sure you hold on to it for when you reach the chopper.
Other than that, it can take a bit of luck and/or skill, but either one will get you 20 GamerPoints.
Koei mixes it up a bit by fusing the Dynasty Warriors and the Samurai Warriors together, but this is still a retread of the gameplay we’ve seen for years in Koei’s games, albeit with a new enemy.
