There are 12 new Trophies in this DLC.

Bronze

Amateur Puzzler
Complete Puzzles 1-7

Detective
Complete Puzzles 8-15

Super Sleuth
Complete Puzzles 16-20

Damage Dodger
Complete Puzzle 6 without taking damage

Pain Prevention
Complete Puzzle 5 without taking damage

Odynophobiac
Complete Puzzle 11 without taking damage

Economical
Complete Puzzle 3 but have at least 1 item left in your inventory that isn't Skip Go or Surrender

Thrifty
Complete Puzzle 17 but have at least 1 item left in your inventory that isn't Skip Go or Surrender

Lightfoot
Complete Puzzle 15 before Sudden Death kicks in

Ain't Got Time to Speed
Complete Puzzle 19 before Sudden Death kicks in

Done in 20 Seconds
Complete Puzzle 18 before Sudden Death kicks in

Silver

Gnat's Nostril
Complete Puzzle 20 but have at least 1 item left in your inventory that isn't Skip Go or Surrender

http://www.ps3trophies.com/forums/ps3-trophy-news/64701-worms-2-armageddon-puzzle-pack-dlc-trophy-list.html