Here is the full list of all 41 Ice Age 4: Continental Drift - Arctic Games trophies - there are 30 bronze, 6 silver, 4 gold and 1 platinum.
Obtain every other trophy in the game.
Finish a Bob-Smashing race in Story Mode.
Finish a Glacier Hopping race in Story Mode.
Finish a Coconut Slingshot game in Story Mode.
Finish a Mountain Drift race in Story Mode.
Finish a Shell Slide game in Story Mode.
Finish a Scrat Cannon game in Story Mode.
Finish a Slip Slide race in Story Mode.
Finish a Ice Smash game in Story Mode.
Finish a Style Jump game in Story Mode.
Finish a Prehistoric Plumber game in Story Mode.
Break every wall of your team without breaking any wall of the opposing team in a Bob-Smashing race.
Collect every Acorn in Glacier Hopping.
Pass through every gate in a single Mountain Drift race.
Place all your shells on the target in one round of Shell Slide.
Reach the end of the level bouncing 20 times or less in Scrat Cannon.
Finish a Slip Slide race without hitting any snow patches.
Collect all acorns and reach the goal in under 1:00 minute in Ice Smash.
Successfully complete 8 tricks in a single Style Jump game.
Find the hidden Acorn in the Scrat Cannon event.
Obtain a Gold Acorn score in Bob-Smashing (Free Play only).
Obtain a Gold Acorn time in Glacier Hopping (Free Play only).
Obtain a Gold Acorn score in Coconut Slingshot (Free Play only).
Obtain a Gold Acorn time in Mountain Drift (Free Play only).
Obtain a Gold Acorn score in Shell Slide (Free Play only).
Obtain a Gold Acorn score in Scrat Cannon (Free Play only).
Obtain a Gold Acorn time in Slip Slide (Free Play only).
Obtain a Gold Acorn time in Ice Smash (Free Play only).
Obtain a Gold Acorn score in Style Jump (Free Play only).
Obtain a Gold Acorn score in Prehistoric Plumber (Free Play only).
Fly 500 miles over land or sea.
Destroy all targets in Coconut Slingshot.
Place a shell in the exact center of the target, without steering it or hitting any other shell.
Win a Tournament against a friend.
Fall into the water 15 times with either Diego or Shira.
Collect 1000 acorns.
Slide down 1000 miles of ice or snow.
Finish the Story mode while playing on the Crew's side.
Finish the Story mode while playing on the Herd's side.
Get a Gold Acorn on every single game event.
Finish Story mode without losing a single game event.