Full list of all 30 XCOM: Enemy Within achievements worth 1,000 gamerscore. It takes around 30-35 hours to unlock all of the achievements on Xbox 360.
Beat the game without buying a Squad Size upgrade (Classic+ difficulty)
Designate a highly decorated soldier as the Volunteer
Kill an enemy as it is psionically attacking you in single player
Field a squad consisting entirely of augmented soldiers and SHIVs (min. 4) and win the mission
Field a squad with 4 augmented soldiers, each with a different base ability and win the mission
Field a squad where all members have at least two modifications (min. 4) and win the mission
Complete Furies
Get a Soldier to have 5 modifications in single player
Kill a Muton Berserker in melee combat in single player
Complete Deluge
Kill an elite enemy Medic with explosive damage in single player
Eliminate all alien waves
Get at least 4 kills with XCOM Base Security personnel
Deal with the newest global threat
Make certain of the new threat's location
Proc Combat Rush on the entire squad (min. 4)
Eliminate an enemy's shield and kill it on the same turn in single player
Kill an unseen enemy detected by a specially modified soldier in single player
Eradicate the infestation
Have your special-duty soldier kill three enemies in the same mission
Cause an enemy to suicide
Field a fully enhanced squad and win the mission
Deploy three tactical subsystems on a single soldier in single player
Kill an elite enemy Sniper with one of your own snipers in single player
Jump two stories in one move in single player
Use Collateral Damage to blow up a car in single player
Beat a new special mission without losing any assets
Augment a soldier in single player
Modify a soldier in single player
Stop a squad member from suffocating in single player