There are 12 new Trophies in this DLC.

Bronze

Last Worm Scout
Complete Retro 1 without the Mayor taking damage

Can't Be Rocked
Complete Retro 5 without taking damage

An Apple a Day…
Complete Retro 8 without picking up a Health Crate

Worminator
Complete Retro 9 and kill all the enemy worms

Leave No Worm Behind
Complete Retro 12 with all 3 player worms alive

We Don't Need Roads
Complete Retro 13 without using the Bridge Kit

Crate Fishing
Collect all the crates on Retro 15

Modernist
Complete Retro 1-5

So Last Year
Complete Retro 6-10

Stuck in the 90s
Complete Retro 11-15

Retrograde!
Complete Retro 16-20

Silver

Child's Play
Complete Retro 14 without the Toy Master taking damage

http://www.ps3trophies.com/forums/ps3-trophy-news/64705-worms-2-armageddon-retro-pack-dlc-trophy-list.html