Successfully complete one of the following tasks to get a trophy:

Goblin Hunter (Bronze): Kill 1,000 goblins.
Thank You For Being a Friend (Bronze): Finish Co-Op campaign (any MP campaign).
Solid Gold (Silver): Have 100,000 gold in your bag at one time.
Man at Arms (Silver): Collect one of every weapon in the game.
Four of a Kind (Silver): Reach level 10 with all character classes.
The Big Stick (Gold): Deal 75 damage with a single attack.

Additionally, there are six secret trophies:

Welcome to Tethyamar (Bronze): Complete Tutorial - Descent into Darkness.
Left in Ruins (Bronze): Complete Chapter 1 - Ruins of Tethyamar.
Into the Deep (Bronze): Complete Chapter 2 - The Depths.
Open Wide (Bronze): Complete Chapter 3 - The Mouth of the Void.
Raze the Dalelands (Bronze): Complete Chapter 4 - The Altar of Bane.
Iron Man (Silver): Log 24 Hours of gameplay.