To unlock PlayStation 3 trophy rewards, complete the following tasks!

Trophy	How to unlock
A Good Dam Fight (Silver)	Defeat the Battlelord on the Hoover Dam.
Air-Duke (Silver)	Win air hockey with a score of 7-0 in the strip club.
Annihilation (Bronze)	Kill 100 aliens.
Balls of Steel (Silver)	Earn a 1,000,000 pinball score in SP.
Baron von Nukem (Bronze)	Shoot down 20 alien fighters.
Beating the One-Eyed Worm (Silver)	Defeat the Leech.
Big Guns, Big Ships (Bronze)	Blow up 5 enemy Gunships or Dropships.
Bucket Head (Bronze)	Find all 3 helmets in the SP campaign.
Call Waiting (Silver)	Listen to all phone messages.
Come Get Some (Gold)	Complete the SP campaign on Hard Difficulty.
Companion Barrel (Bronze)	Unlock the secret closet at the end of the Forkstop.
Damn, I'm Good (Gold)	Complete the SP campaign on Insane Difficulty.
Dead Useful (Bronze)	Kill 10 aliens with environmental explosives.
Drawrings (Bronze)	Doodle something on the whiteboard in SP.
Duke Angry, Duke SmasH! (Bronze)	Kill 15 aliens with melee attacks while on steroids.
Extermination (Bronze)	Kill 50 aliens.
Flagon of Chuckles (Bronze)	Drink a beer in SP.
Fork the Pork (Bronze)	Kill 6 aliens with the forklift.
Freeze Well! (Bronze)	Kill 15 frozen aliens.
Full Body Tourettes (Bronze)	Get knocked down 10 times.
Gunslinger (Silver)	Carry the gold pistol through the whole SP campaign.
He's Got a Hologram! (Bronze)	Use a Holoduke in SP.
Hippy-Stomper (Bronze)	Foot stomp 12 aliens.
I Am All That Is Man (Silver)	Discover all ego cap rewards.
I Need a Date (Bronze)	Look at every page of a calender in SP.
I Need a Towel (Bronze)	Get hit by 10 Pregnator bombs.
Judge, Jury, Executioner (Bronze)	Execute 20 aliens.
Juiced (Bronze)	Take steroids in SP.
Let's Rock (Silver)	Complete the SP campaign on Normal Difficulty.
Lots of Whacking (Bronze)	Win a game of Alien Abortion in the strip club.
Natural Disaster 3x (Bronze)	Kill 3 aliens at once.
Nobody Likes a Whiner (Bronze)	Knock out the talent at the talk show.
Noms (Bronze)	Eat 10 pieces of food in SP.
Not Bad for a Human (Silver)	Defeat the Alien Queen.
Nuclear Devastation (Bronze)	Kill 250 aliens.
Octacide (Silver)	Defeat the Octaking.
On the Noggin' (Bronze)	Kill 30 aliens with headshots.
One-Eyed Freak (Bronze)	Defeat the Cycloid.
Party Animal (Bronze)	Drink all of the beers in the strip club.
Pescaphobe (Bronze)	Kill all of the catfish in the underwater level.
Piece of Cake (Bronze)	Complete the SP campaign on Easy Difficulty.
Pit Champion (Bronze)	Defeat the Battlelord in Las Vegas.
Road Rage (Bronze)	Kill 15 aliens with the monster truck.
Savior of the Universe (Platinum)	You got them all.
Special Thanks (Bronze)	Watch the credits all the way through.
Sticky Bomb Like You! (Bronze)	Put a Trip Mine on a live alien.
Substance Abuser (Bronze)	Drink beer while on steroids or vice-versa in SP.
Sunday, Black Sunday (Bronze)	Shoot down the blimp above the stadium.
Tosser...in the Literal Sense (Bronze)	Kill 10 aliens with tossed objects.
Trapper (Bronze)	Kill 10 aliens with Trip Mines.
Turd Burglar (Bronze)	Find and steal a piece of poo.