Upon receiving the mission you also receive a special item with which to destroy the cocoons.
This is the only way to attack a cocoon in this mission. Guns, pets, bishslapping, nothing else works. (Yes, I've tried..)
The mission is in the same ship as several of the other mission types so head out to ICC and go by the Unicorn shuttle to the outpost.
It is strongly recommended to buff up before entering the mission as you will spawn in a populated hallway and potentially can be attacked very shortly after zoning in.
While most mobs are stationary some will be patrolling their area of responsibility so it is advisable to study the minimap before going through doors or entering combat.
Removing the crew is not difficult (apart from surviving the fight, some of those aliens pack quite a punch) since they have to be in close proximity to alert each other. The roving mobs are a higher risk since their movement may take them close enough.
The hallways are long - it seems to be a rather large ship - but there are no problem navigating them.
However, I almost always find a couple of mobs that are standing just behind an open door leading away from the passageway, these mobs will aggro when I pass by so again, it pays to pay attention to the minimap.
I always remove the crew from the ship first, then proceed to terminate the cocoons one at a time, dispatching the larvae as they spawn - helped by the fact that they will aggro me immediately unless I'm halfway across the minimap. These larvae also pack quite a punch so squishy toons need to be careful.
This is what the cocoons look like:
Once you have terminated 10 cocoons the special item disappears and you get a new mission, to return and report to the Alien Handler.
Not that there's much reporting back going on - just tell him you completed the mission and you get your reward.
A thing to note is that exiting the ship will cause the mission to reset, meaning that the crew will come back and the (invisible) cocoon counter will be reset so you can't kill 9 cocoons, exit the ship and then just kill one more to complete the mission.
Worth knowing for those toons that struggle to handle the crew. However, a little thinking and planning will give you a chance to accomplish the mission goal, even on a gimpy toon.
(Hint: it's all about finding the cocoons with the fewest guards around.)
Edit 2012 September 01:
The special item seems to be persistent now so it won't remove itself from your inventory.
Meaning that now you only have the new return-mission to tell you that you've done the job properly. Aside, that is, from your ability to count to ten..