A quick way to boost this in multiplayer is on 1 vs. 1 Team Deathmatch (map is Last Hope) and have the player using the alien become the Crusher. This is done by receiving a prompt to "press unleash the crusher" when near a "hive" location. There are 2 along the path under the bridge in the middle of the map. To the alien, these will have a real bright yellow/green highlight to them (one located next to a forklift). Once transformed, the marine (who's trying to earn this achievement) must shoot the body (explosives speed this up to) to kill it. Remember the head is nearly invincible and your friend shouldn't damage you for this achievement.
Towards the end of mission 9 (Hope in Hadley's) there is a fight with a crusher if you'd like to attempt this in campaign. Once it appears, find high ground (hill, slope, crate) to avoid damage from it. Kill using your explosives and shooting the body. You must get the kill for this to count. Use restart checkpoint to your advantage if you're damaged by it or don't get the kill. Remember the head is invulnerable. This is easier in co-op to have someone distract it. The AI can still steal your kill, so be aware.
Be sure to listen to the explanation while watching the video from azGRIMES:
Just got this on Mission 9 Hope in Hadley's and pretty simple to do. Every object in the area that you can take cover behind can be destroyed by the crusher when he charges into it...except for the apc. Just keep circling around it and use explosives or shoot any part of it you can that the head isn't covering, I had to use ripley's flamethrower and that killed it pretty easily.