Here is the full list of all 15 Polar Panic trophies - there are 13 bronze, 1 silver and 1 gold.
Score 1,500,000 points in 1 player Survivor mode
Complete the Puzzle Mode
Complete the Story mode on Insane difficulty
Get an A grade for a Story Mode Chapter
Complete a Chapter in Story Mode without losing a life
Collect all the snowmen and break the cages in Story Mode
Complete the Story Mode
Collect all 10 extra life pick-ups
Destroy 50 trapper generators
Kill all the trappers on a boat level by only using the barrels
Kill a trapper with a sliding block over 15 grid squares away (not achievable in Multiplayer)
Get an AA grade in 10 Puzzle Mode levels
Achieve a 10x Combo bonus (not achievable in Multiplayer)
Survive 5 waves on all 5 levels of 1 player Survivor mode
Kill a trapper of each type (not achievable in Multiplayer)