Bronze:

Bought a Slot
Objective: Bought one Plasmid or Tonic Slot at a Gatherer's Garden.

Max Plasmid Slots
Objective: Fully upgraded to the maximum number of Plasmid Slots.

Upgraded a Weapon
Objective: Upgraded a weapon at a Power to the People Station.

Fully Upgraded a Weapon
Objective: Installed the third upgrade to a weapon.

All Weapon Upgrades
Objective: Found every Power to the People weapon upgrade in the game.

Prolific Hacker
Objective: Hacked one of each kind of machine.

Master hacker
Objective: Hacked 30 machines at a distance with the Hack Tool.

First Research
Objective: Researched a Splicer with the Research Camera.

One Research Track
Objective: Maxed out one Research Track.

Research Master
Objective: Completed all research on every subject in Rapture.

Fully Upgraded a Plasmid
Objective: Fully upgraded one Plasmid to the Level 3 version.

All Plasmids
Objective: Found or purchased all 11 basic Plasmid types.

Trap Master
Objective: Killed 30 enemies using only Traps.

Master Protector
Objective: Got through a Gather with no damage and no one getting to the Little Sister.

Big Spender
Objective: Spent 2000 dollars at Vending Machines.

Welcome to Rapture
Objective: Completed your first non-private match.

Unnatural Selection
Objective: Scored your first kill in a non-private match.

Disgusting Frankenstein
Objective: Become a Big Daddy for the first time in a non-private match.

'Mr. Bubbles - No!'
Objective: Took down your first Big Daddy in a non-private match.

Against All Odds
Objective: Finished the game on the hardest difficulty level.

Two-Bit Heroics
Objective: Complete your first trial in a non-private match.

Mother Goose
Objective: Saved your first Little Sister in a non-private match.

Parasite
Objective: Achieved Rank 10.

Little Moth
Objective: Achieved Rank 20.

Skin Job
Objective: Achieved Rank 30.

Man About Town
Objective: Played at least one non-private match on each multiplayer map.

Silver:

Grand Daddy
Objective: Defeated 3 Big Daddies without dying during the fight.

Master Gatherer
Objective: Gathered 600 ADAM with Little Sisters.

Dealt with Every Little Sister
Objective: Dealt with every Little Sister.

Big Brass Balls
Objective: Finished the game without using Vita-Chambers.

Rapture Historian
Objective: Found 100 audio diaries.

Proving Grounds
Objective: Won your first non-private match.

Gold: