The list of Xbox 360 achievements for BioShock Infinite have appeared online, but gander at your own risk, because I hear there are spoilers.

Tin Soldier (10 points) - Completed the game on Easy difficulty or above.
Saw the Elephant (25 points) - Completed the game on Normal difficulty or above.
Stone Cold Pinkerton (50 points) - Completed the game on Hard difficulty or above.
Auld Lang Syne (75 points) - Completed the game on 1999 mode.
Should Auld Acquaintance... (10 points) - Unlocked 1999 mode.
Industrial Accident (5 points) - Killed 20 enemies with a Sky-Hook Execution.
Aerial Assassin (5 points) - Killed 20 enemies with a Sky-Line Strike.
A Real Pistol (5 points) - Killed 25 enemies with the Broadsider Pistol.
Passionately Reciprocated (5 points) - Killed 150 enemies with the Founder Triple R Machine Gun or Vox Repeater.
Street Sweeper (5 points) - Killed 50 enemies with the Founder China Broom Shotgun or Vox Heater.
Big Game Hunter (5 points) - Killed 100 enemies with the Founder Huntsman Carbine or Vox Burstgun.
Loose Cannon (5 points) - Killed 25 enemies with the Paddywhacker Hand Cannon.
On a Clear Day... (5 points) - Killed 30 enemies with the Bird's Eye Sniper Rifle.
Here Little Piggy (5 points) - Killed 30 enemies with the Founder Pig Volley Gun or Vox Hail Fire.
Master of Pyrotechnics (5 points) - Killed 20 enemies with the Barnstormer RPG.
Seasoned to Taste (5 points) - Killed 30 enemies with the Peppermill Crank Gun.
Well Rounded (10 points) - Used all 8 Vigors against enemies.
Vigorous Opposition (50 points) - Killed 75 enemies either with a Vigor or while the enemy is under the effects of a Vigor.
More for Your Money (25 points) - Lured 3 enemies into a single Vigor trap 5 times.
Combination Shock (50 points) - Performed all 8 of the Vigor combinations.
Mind Over Matter (10 points) - Killed 20 enemies using Possessed machines.
Tear 'em a New One (25 points) - Opened 30 Tears.
Strange Bedfellows (10 points) - Killed 20 enemies using allies brought in through a Tear.
On the Fly (10 points) - Killed 30 enemies while riding a Sky-Line.
Bolt From the Blue (25 points) - Killed 5 enemies with a headshot while riding a Sky-Line.
Hazard Pay (25 points) - Killed 10 enemies by utilizing environmental hazards.
Bon Voyage (25 points) - Killed 20 enemies by knocking them off Columbia.
Skeet Shoot (25 points) - Killed 5 enemies while they are falling.
Lost Weekend (10 points) - Killed 5 enemies while you are drunk.
David & Goliath (10 points) - Killed 20 "Heavy Hitter" enemies.
Heartbreaker (50 points) - Killed a Handyman by only shooting his heart.
Dress for Success (5 points) - Equipped a piece of Gear in all four slots.
Kitted Out (10 points) - Fully upgraded one weapon and one Vigor.
Raising the Bar (10 points) - Upgraded one attribute (Health, Shield, or Salts) to its maximum level.
Infused with Greatness (25 points) - Collected every Infusion upgrade in a single game.
Sightseer (50 points) - Used all telescopes and Kinetoscopes in the game.
The Roguish Type (25 points) - Used Elizabeth to pick 30 locks.
Eavesdropper (50 points) - Collected every Voxophone.
Grand Largesse (10 points) - Spent $10,000 at the vending machines of Columbia.
Coins in the Cushion (10 points) - Looted 200 containers.
Scavenger Hunt (75 points) - Completed the game in 1999 mode without purchasing anything from a Dollar Bill vending machine.

Along with those listed above, there are also nine secret achievements.

Thanks to Mike Bendel for the news tip, and the spoiler warning!

[via ExoPhase and Xbox360Achievements.org]