What are the hidden achievements in XCOM: Enemy Unknown?

Solution 1:

You can see the full list of Steam achievements at the steam site.

Out of the 60 achievements there are 20 that don't have a description. 10 of them are plot related achievements and you will unlock all of them (except from the Firestorm one) if you finish the original game:

• Prisoner of War: Capture a live alien.
• The Gatekeeper: Stun an Outsider.
• X Marks the Spot: Uncover the alien base's location.
• Off My Planet: Recover the Hyperwave Beacon.
• Ride the Lightning: Build a Firestorm. (not essential for the plot)
• See All, Know All: Build the Hyperwave Relay.
• Beyond the Veil: Find a soldier with the Gift.
• And Hell's Coming With Me: Successfully assault an Overseer UFO.
• On the Shoulders of Giants: Build the Gollop Chamber.
• The Volunteer: Make contact with the Ethereal hive mind.

UPDATE:

There are 10 more that don't have a description, 5 of them are related to the slingshot DLC, those are:

• New Friend: Complete Friends in Low Places.
• Bait the Hook: Complete Confounding Light.
• The Bigger They Are: Complete Gangplank.
• Rising Dragon: Take your new ally into the final challenge.
• All Aboard: Complete Confounding Light with more than 3 turns left on the timer.

The other 5 do not appear on the xbox 360 version or the PS3 version, and have 0% completion, which means that nobody was able to get them, just as it was with the above 5 before the release of the slingshot DLC, those are:

• Disaster Averted: Complete Deluge.
• The Chase Is On: Complete Portent.
• Great Minds Think Alike: Complete Furies.
• No Sweat: Complete Deluge without activating more than 2 valves.
• Saved to Savior: Have your newest ally volunteer for the most difficult duty.

As you can see, their description, taken from here, makes no sense regarding to the game. With the history regarding the slingshot DLC they are probably related to a future DLC.

Solution 2:

Need to get more info on this as I've got 33 of 60. And can see some that haven't been achieved, but not all of them.

Here's the one's I know:

• Ain't No Cavalry Comin': Have a soldier survive every mission in a full game.
• All Employees Must Wash Hands…: In a single game, complete every Autopsy.
• All Together Now: Get satellite coverage over every country on one continent.
• And Hell's Coming With Me: Successfully assault an Overseer UFO.
• And So It Begins…: Complete the tutorial mission.
• Angel of Death: Kill an alien while flying. Single player only.
• As A Scalpel: Earn the "Excellent" rating in every performance category on a terror mission.
• Bada Boom: Kill 50 aliens with explosive weapons.
• Beyond the Veil: Find a soldier with the Gift.
• Bubonic: Play a multiplayer match against someone with this achievement.
• Combat Ready: Build an item.
• A Continental Fellow: Win the game from each of the 5 starting locations.
• Drums in the Deep: Gain access to the lowest level in your base.
• Earth First: Beat the game on Classic difficulty.
• Edison: In a single game, complete every Research Project.
• Eye in the Sky: Launch a Satellite.
• Flight of the Valkyries: Win a mission with an all-female squad. Single player only.
• The Gatekeeper: Stun an Outsider.
• Happy to Oblige: Fulfill a Council request.
• The Hardest Road: Advance one of your soldiers to Colonel rank.
• Humanity's Savior: Beat the game on any difficulty.
• Hunter/Killer: In a single game, shoot down one of each alien craft.
• Lone Wolf: Clear a UFO crash site with one soldier on Classic or Impossible difficulty.
• Man No More: Build a suit of powered armor.
• Meet New People. Then Kill Them.: Win a multiplayer match.
• No Looking Back: Beat the game in Ironman mode on Classic or Impossible Difficulty.
• Off My Planet: Recover the Hyperwave Beacon.
• On the Shoulders of Giants: Build the Gollop Chamber.
• One Gun at a Time: Staff the Engineering Department with 80 engineers.
• Oppenheimer: Staff the Research Labs with 80 scientists.
• Our Finest Hour: Beat the game on Impossible difficulty.
• Pale Horse: Kill 500 aliens.
• Prisoner of War: Capture a live alien.
• Ride the Lightning: Build a Firestorm.
• See All, Know All: Build the Hyperwave Relay.
• Shooting Stars: Shoot down 40 UFOs.
• Skunkworks: In a single game, complete every Foundry project.
• Tables Turned: Shoot down a UFO.
• Theory...: Build a Laboratory.
• ...and Practice.: Build a Workshop.
• Up and Running: Build a base facility.
• The Volunteer: Make contact with the Ethereal hive mind.
• We Happy Few: Complete a mission without losing a soldier.
• Welcoming Committee: Kill 150 aliens.
• Wet Work: Complete a Very Hard abduction mission in five turns or less on Classic or Impossible difficulty.
• What Wonders Await: Complete a Research Project.
• Worth Every Penny: Acquire 1000 credits in one month.
• X Marks the Spot: Uncover the alien base's location.
• Xavier: Mind Control an Ethereal. Single player only.
• You Have 5 Seconds to Comply: Build a S.H.I.V.