Bronze

Bought a Slot
Bought one Plasmid or Tonic Slot at a Gatherer’s Garden.

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

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

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

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

Prolific Hacker
Hacked one of each kind of machine. 

Master Hacker
Hacked 30 machines at a distances with the Hack Tool.

First Research
Researched a Splicer with the Research Camera. 

One Research Track
Maxed out one Research Track. 

Research Master
Completed all research on every subject in Rapture. 

Welcome to Rapture
Completed your first non-private match. 

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

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

“Mr. Bubbles– No!”
Took down your first Big Daddy in a non-private match. 

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

Two-Bit Heroics
Completed your first trial in a non-private match.

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

Parasite
Achieved Rank 10.

Little Moth
Achieved Rank 20. 

Skin Job
Achieved Rank 30.

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

All Plasmids
Found or purchased all 11 basic Plasmid types. 

Trap Master
Killed 30 enemies using only Traps. 

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

Big Spender
Spent 2000 dollars at Vending Machines. 

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

Silver

Dealt with Every Little Sister
Dealt with every Little Sister.

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

Rapture Historian
Found 100 audio diaries.

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

Master Gatherer
Gathered 600 ADAM with Little Sisters.

Proving Grounds
Won your first non-private match.

Gold

Choose the Impossible
Achieved Rank 40.

Platinum

Platinum
Unlocked all trophies.

There are also 17 secret trophies, totaling to the usual 51 trophies.