There are 27 Trophies that can be earned in this title.

Bronze

Any way up
Cause 69 damage to an enemy Worm.

Six Pest
Kill 6 enemy worms in a single turn.

Prod for Victory
Win a game by using the Prod.

I'll Try Anything Once
Use every weapon and utility in the game once.

Drop Your Load
Kill a worm in a Ranked Match by dropping a weapon from the Jet-Pack or Ninja Rope.

Happy Shopper
Collect more than 10 Weapon Crates in a single Ranked Match.

Six Dollar Worm
We can rebuild him! Collectt 6 Health Crates with one worm during a Ranked Match.

Martyn's Missus
Spend more than 2000 cash unlocking items in the shop.

Teacher's Pet
Complete all tutorials.

Name and Fame
Name a team and choose hats, speech-banks, gravestones and victory dances for them.

Silver

Mine Gott!
Detonate at least 3 Mines during one turn in a Ranked Match.

Get Your Lob On
Win and Playstation Network game using just the Grenade.

In Your Own Time
Win a Ranked Match by being the last surviving worm not killed by the rising water in Sudde Death.

Cheeky Flocker
Deploy 25 Sheep in any ranked games.

Oldest Swinger inTown
Use the ninja rope 1000 times.

Wind Assisted
Win a Ranked Match using only the Bazookas.

Fire Starter
Use the fire weapons 200 times.

Ded-Eye Dick
Inflict maximum damge on an enemy worm with a weapon during a Ranked Match.

Mine's a Drink
Knock an enemy worm into the water using only a Mine in a Ranked Match.

Gold

Going Solo
Complete the Single Player Campaign.

Mine All Mine!
Detonate at least 5 Mines during one turn in a Ranked Match.

Collateral Damage
Inflict more than 150 damage on a single enemy worm by detonating at least one barrel.

Ranked Master
Achieve 17 wins in each of the following ranked game modes: Standard, Pro, Crazy Crates and Fort.

One Good Turn…
Inflict maximum damage on an enemy worm the turn after they've inflicted maximum damage on one of your worms during a Ranked Match.

Armageddon Good At This!
Win a Ranked Match by being the last worm standing after deploying Armageddon.

Donkey Dodger
Survive the enemy deploying a Concrete Donkey in a Ranked Match and go on to win the round.

Platinum

Worms Elite
Easy, just unlock all the other trophies!

http://www.ps3trophies.org/game/worms-2-armageddon/trophies/