There are 51 Trophies that can be collected.

BRONZE

Goliath, Meet David
Allowed a Goliath to level up four times before killing him

Went Five Rounds
Completed Round 5 of any Circle of Slaughter

Not Quite Dead
Reached level 5

Better Than You Were
Reached level 10

Arctic Explorer
Discovered all named locations in Three Horns, Tundra Express, and Frostburn Canyon

Urban Explorer
Discovered all named locations in Sanctuary, Opportunity, and Lynchwood

Highlands Explorer
Discovered all named locations in The Highlands, Thousand Cuts, and Wildlife Exploitation Preserve

Blight Explorer
Discovered all named locations in Eridium Blight, Arid Nexus, and Sawtooth Cauldron

Sugar Daddy
Tipped Moxxi $10,000

Decked Out
Had Purple-rated gear or better equipped in every slot

Sabre Rattler
Killed 100 enemies with the Sabre turret

Phased and Confused
Phaselocked 100 enemies

So Much Blood!
Gunzerked continuously for 90 seconds

Cute Loot
Killed a Chubby

Tribute To A Vault Hunter
Got an item from Michael Mamaril

Definitely An Italian Plumber
Killed Donkey Mong

High-Flying Hurler
Killed a flying enemy with a thrown Tediore weapon

Token Gesture
Redeemed 25 tokens

Unseen Predator
Remained in Zero's Deception mode for ten seconds straight

Build Buster
Killed a Constructor without it ever building another bot

How Do I Look?
Unlocked 10 customization items

Friendship Rules
Revived someone from "Fight for Your Life!" that is on your friends list

Better Than Money
Purchased 5 items from the black market

Up High, Down Low
Gave Claptrap a high five

Bounty Hunter
Completed 20 side missions

SILVER

Always Improving
Reached level 25

Capped Out…For Now
Reached level 50

World Traveler
Discovered all named locations

Did It All
Completed all side missions

GOLD

Challenge Accepted
Completed level 1 of all non-level-specific challenges with a single character

PLATINUM

Borderland Defender Round Two
Unlocked all Borderlands 2 trophies

20 SECRET

http://www.ps3trophies.org/game/borderlands-2/trophies/