Accomplish the indicated achievement to get the corresponding number of Gamerscore points:

Bought a Slot (5 points): Buy one Plasmid or Tonic Slot at a Gatherer's Garden.
Max Plasmid Slots (10 points): Fully upgrade to the maximum number of Plasmid Slots.
Upgraded a Weapon (10 points): Upgrade any weapon at a Power to the People Station.
Fully Upgraded a Weapon (10 points): Install the third and final upgrade to any of your weapons.
All Weapon Upgrades (20 points): Find all 14 Power to the People weapon upgrades in the game.
Prolific Hacker (20 points): Successfully hack at least one of every type of machine.
Master Hacker (20 points): Hack 30 machines at a distance with the Hack Tool.
First Research (5 points): Research a Splicer with the Research Camera.
One Research Track (20 points): Max out one Research Track.
Research Master (20 points): Max out research on all 9 research subjects.
Grand Daddy (25 points): Defeat 3 Big Daddies without dying during the fight.
Master Gatherer (30 points): Gather 600 ADAM with Little Sisters.
Fully Upgraded a Plasmid (10 points): Fully upgrade one of your Plasmids to the level 3 version at a Gatherer's Garden.
All Plasmids (20 points): Find or purchase all 11 basic Plasmid types.
Trap Master (15 points): Kill 30 enemies using only Traps.
Master Protector (15 points): Get through a Gather with no damage and no one getting to the Little Sister.
Big Spender (15 points): Spend 2000 dollars at Vending Machines.
Dealt with Every Little Sister (50 points): Either Harvest or Save every Little Sister in the game.
Against All Odds (30 points): Finish the game on the hardest difficulty level.
Big Brass Balls (25 points): Finish the game without using Vita-Chambers.
Rapture Historian (40 points): Find 100 audio diaries.
Unnatural Selection (10 points): Score your first kill in a non-private match.
Welcome to Rapture (10 points): Complete your first non-private match.
Disgusting Frankenstein (10 points): Become a Big Daddy for the first time in a non-private match.
"Mr. Bubbles - No!" (20 points): Take down your first Big Daddy in a non-private match.
Mother Goose (20 points): Save your first Little Sister in a non-private match.
Two-Bit Heroics (10 points): Complete your first trial in a non-private match.
Parasite (10 points): Achieve Rank 10.
Little Moth (20 points): Achieve Rank 20.
Skin Job (20 points): Achieve Rank 30.
Choose the Impossible (50 points): Achieve Rank 40.
Proving Grounds (20 points): Win your first non-private match.
Man About Town (10 points): Play at least one non-private match on each multiplayer map.

Additionally, there are seventeen secret achievements:

Daddy's Home (10 points): Found your way back into the ruins of Rapture.
Protector (20 points): Defended yourself against Lamb's assault in the train station.
Sinclair’s Solution (20 points): Joined forces with Sinclair in Ryan Amusements.
Confronted Grace (10 points): Confronted Lamb’s lieutenant in Pauper’s Drop.
Defeated the Preacher (20 points): Defeated the Preacher.
Nose for News (20 points): Uncovered the secret of Dionysus Park.
Found Lamb's Hideout (20 points): Gained access to Lamb’s stronghold.
Reunion (50 points): Reunited with your original Little Sister.
Heading to the Surface (25 points): Headed to the surface on the side of Sinclair's escape pod.
Escape (100 points): Escaped Rapture.
9-Irony (5 points): Paid your respects to the founder of Rapture.
Distance Hacker (5 points): Used the Hack Tool to hack an object at a distance.
Unbreakable (20 points): Defended yourself against the Big Sister without dying.
Look at You, Hacker (15 points): Killed 50 enemies using only hacked Security.
Adopted a Little Sister (5 points): Adopted a new Little Sister for the first time.
Savior (25 points): Saved every Little Sister and spared Grace, Stanley and Gil.
Counterattack (5 points): Killed an enemy with its own projectile.