The following six types of alien ships must be shot down during the same playthrough.
Choose a soldier at the Gene Mods lab and modify his legs with "Muscle Fiber Density". In the next mission, that soldier will be able to jump two stories high.
 The Bulldozer must be on fire for about ten seconds. This can be done in the Cook Off job on Overkill. Wait for him to enter the house.,then flame him from behind the kitchen counter. Have support with Molotov cocktails from upstairs to keep him on fire.
Successfully stun an Exalt-Agent with the Arc-Thrower. Do this by shooting the agent down to less than 3 points of health, then move close to him and use the Arc-Thrower.
The "special-duty" soldier is the one that is sent out alone on covert missions. When your team goes to extract him, ensure he gets three kills.
Use a MEC Trooper with the Kinetic Strike module.
Upgrade one of your MECs to level 3.
Note: This requires Enemy Within. The "Seeker" robotic flying squid has a strangling attack. Kill a Seeker strangling your squad member it kills them.
Kill an alien revealed by a nearby teammate with the Bioelectric Skin gene modification. The rest of your team should not be able to see the alien, and kill it with a rocket, grenade, or other weapon.