BioShock Infinite has 70 achievements worth 1420 gamerscore

Tin Soldier 0 Completed the Main Campaign on Easy difficulty or above.	10
Saw the Elephant 0 Completed the Main Campaign on Normal difficulty or above.	25
Stone Cold Pinkerton 0 Completed the Main Campaign on Hard difficulty or above.	50
Auld Lang Syne 0 Completed the Main Campaign on 1999 Mode.	75
Should Auld Acquaintance... 0 Unlocked 1999 Mode.	10
Industrial Accident 0 In the Main Campaign, killed 20 enemies with a Sky-Hook Execution.	5
Aerial Assassin 0 In the Main Campaign, killed 20 enemies with a Sky-Line Strike.	5
A Real Pistol 0 In the Main Campaign, killed 25 enemies with the Broadsider Pistol.	5
Passionately Reciprocated 0 In the Main Campaign, killed 150 enemies with the Founder Triple R Machine Gun or Vox Repeater.	5
Street Sweeper 0 In the Main Campaign, killed 50 enemies with the Founder China Broom Shotgun or Vox Heater.	5
Big Game Hunter 0 In the Main Campaign, killed 100 enemies with the Founder Huntsman Carbine or Vox Burstgun.	5
Loose Cannon 0 In the Main Campaign, killed 25 enemies with the Paddywhacker Hand Cannon.	5
On a Clear Day... 0 In the Main Campaign, killed 30 enemies with the Bird's Eye Sniper Rifle.	5
Here Little Piggy 0 In the Main Campaign, killed 30 enemies with the Founder Pig Volley Gun or Vox Hail Fire.	5
Master of Pyrotechnics 0 In the Main Campaign, killed 20 enemies with the Barnstormer RPG.	5
Seasoned to Taste 0 In the Main Campaign, killed 30 enemies with the Peppermill Crank Gun.	5
Well Rounded 0 In the Main Campaign, used all 8 Vigors against enemies.	10
Vigorous Opposition 0 In the Main Campaign, killed 75 enemies either with a Vigor or while the enemy is under the effects of a Vigor.	10
More for Your Money 0 In the Main Campaign, lured 3 enemies into a single Vigor trap 5 times.	25
Combination Shock 0 In the Main Campaign, performed all 8 of the Vigor combinations.	50
Mind Over Matter 0 In the Main Campaign, killed 20 enemies using Possessed machines.	10
Tear 'em a New One 0 In the Main Campaign, opened 30 Tears.	25
Strange Bedfellows 0 In the Main Campaign, killed 20 enemies using allies brought in through a Tear.	10
On the Fly 0 In the Main Campaign, killed 30 enemies while riding a Sky-Line.	10
Bolt From the Blue 0 In the Main Campaign, killed 5 enemies with a headshot while riding a Sky-Line.	25
Hazard Pay 0 In the Main Campaign, killed 10 enemies by utilizing environmental hazards.	25
Bon Voyage 0 In the Main Campaign, killed 20 enemies by knocking them off Columbia.	25
Skeet Shoot 0 In the Main Campaign, killed 5 enemies while they are falling.	25
Lost Weekend 0 In the Main Campaign, killed 5 enemies while you are drunk.	10
David & Goliath 0 In the Main Campaign, killed 20 "Heavy Hitter" enemies.	10
Heartbreaker 0 In the Main Campaign, killed a Handyman by only shooting his heart.	50
Dress for Success 0 In the Main Campaign, equipped a piece of Gear in all four slots.	5
Kitted Out 0 In the Main Campaign, fully upgraded one weapon and one Vigor.	10
Raising the Bar 0 In the Main Campaign, upgraded one attribute (Health, Shield, or Salts) to its maximum level.	10
Infused with Greatness 0 In the Main Campaign, collected every Infusion upgrade in a single game.	25
Sightseer 0 In the Main Campaign, used all telescopes and Kinetoscopes in the game.	50
The Roguish Type 0 In the Main Campaign, used Elizabeth to pick 30 locks.	25
Eavesdropper 0 In the Main Campaign, collected every Voxophone.	50
Grand Largesse 0 In the Main Campaign, spent $10,000 at the vending machines of Columbia.	10
Coins in the Cushion 0 In the Main Campaign, looted 200 containers.	10
Scavenger Hunt 0 Completed the Main Campaign in 1999 Mode without purchasing anything from a Dollar Bill machine.	75

Secret Achievements

Written in the Clouds 0 In the Main Campaign, completed Lighthouse.	5
Welcome to Monument Island 0 Reached Monument Island.	10
Shock Tactics 0 Retrieved Shock Jockey.	10
First Class Ticket 0 In the Main Campaign, boarded The First Lady.	10
Armed Revolt 0 Assisted the gunsmith.	10
Working Class Hero 0 In the Main Campaign, completed the Factory.	25
Blood in the Streets 0 Completed Emporia.	25
Higher Learning 0 Completed Comstock House.	25
The Bird or The Cage 0 Completed The Hand of the Prophet.	25

BioShock Infinite: Clash in the Clouds

There are 10 achievements with a total of 210 points.

Friendly Skies 0 Defeated all waves in The OPS Zeal.	15
Duke or Dimwit? 0 Defeated all waves in Duke and Dimwit Theater.	15
Rooftop Ruffian 0 Defeated all waves in Raven's Dome.	15
Hand of the Prophet 0 Defeated all waves in Emporia Arcade.	30
Museum Curator 0 In CitC, unlocked all Gallery items.	30
Sergeant-at-Arms 0 In CitC, got a kill with each weapon and vigor (except Bucking Bronco).	15
Rope-a-Dope 0 In CitC, knock an enemy around the city with Undertow, then knock him off the edge of the city.	15
The Ol' One-Two 0 In CitC, used all eight different vigor combos to deliver the killing blow on an enemy.	15
Missile Defense System 0 In CitC, killed an enemy with splash damage by shooting a rocket out of the air.	30
Blue Ribbon Champ 0 In CitC, completed all Blue Ribbon Challenges.	30

BioShock Infinite: Burial at Sea - Episode 1

There are 10 achievements with a total of 250 points.

Audio Enthusiast 0 Collected all Audio Diaries in Burial at Sea - Episode 1.	50
Fully Equipped 0 Purchased any two upgrades for Old Man Winter or Radar Range in Burial at Sea - Episode 1.	10
Confirmed Luddite 0 Destroyed ten Turrets in Burial at Sea - Episode 1.	10
Cook and Serve 0 Made 5 enemies explode with the Radar Range in Burial at Sea - Episode 1.	10
Chain Reaction 0 Damaged fifteen foes with an exploding enemy, using the Radar Range in Burial at Sea - Episode 1.	50
Break the Ice 0 Shattered 5 enemies who had been frozen with Old Man Winter in Burial at Sea - Episode 1.	10
Snowball Effect 0 Froze 2 enemies with the same Old Man Winter trap in Burial at Sea - Episode 1.	10

Secret Achievements

Down in the Briney 0 Took a Bathysphere ride in Burial at Sea - Episode 1.	25
Burial at Sea 0 Completed Burial at Sea - Episode 1.	50
Going Places 0 Rode the tram in Burial at Sea - Episode 1.	25

View all BioShock: The Collection Achievements