Trophies - Successfully complete one of the following tasks to get a trophy:

Adventure is Out There (Bronze): Defeat the first wave of combat planes.
To Paradise Falls (Bronze): Complete the level to start Carl's journey to Paradise Falls.
A Bird Named Kevin (Bronze): Find Kevin before Muntz does.
Slide and Slither (Bronze): Defeat the giant Anaconda.
A Voice In The Mist (Bronze): Find the voice in the mist.
Meet the Pack (Bronze): Meet the pack: Alpha, Beta, and Gamma.
Night in the Jungle (Bronze): Avoid being captured by Muntz's dogs.
Sinkhole Terror (Bronze): Defeat the giant Crocodile.
Paradise Falls (Bronze): Help Carl get his house to the top of Paradise Falls.
Spirit of Adventure (Bronze): Free Russell and Kevin, then escape the Dirigible.
Teamwork Badge (Bronze): Defeat either the giant Anaconda or Crocodile with 2 players.
Wings Badge (Bronze): Defeat the first plane in the battle over Paradise Falls.
Animation Badge (Bronze): Unlock the Bonus Art.
First Aid Badge (Bronze): Use Russell's Canteen three times.
Bird Watching Badge (Bronze): Locate Kevin for the first time.
Defense Badge (Bronze): Successfully defend against 10 dog ambushes.
Fishing Badge (Bronze): Survive against the hungry Piranhas.
Hiking Badge (Bronze): Find the picture-perfect view of Paradise Falls.
Entomology Badge (Bronze): Collect all varieties of each Butterfly and Dio Bug in the game.
Karate Badge (Bronze): Break open 10 watermelons.
Kite Badge (Bronze): Use Carl's House to float across all the chasms in the game.
Sharp Tools Badge (Bronze): Use Russell's key to cut through three items in the game.
Knot Tying Badge (Bronze): Tie off the house so it doesn't float away.
Music Badge (Bronze): Use Russell's Bugle three times.
Recycling Badge (Bronze): Play through any previously completed level in Story Mode.
Shoveling Badge (Bronze): Dig up all of the hidden bones using Dug.
Swimming Badge (Bronze): Swim through all of the areas that have water.
Survivor Badge (Bronze): Complete any Story Mode level without failing or quitting.
Rare Statue Badge (Bronze): Find and collect the Gold Jaguar.
Buddy System Badge (Bronze): Free your buddy from five Snare Traps.
Pest Control Badge (Bronze): Squish 10 Wasps and Spiders.
Bug Hunting Badge (Silver): Catch or squash 100 Dio Bugs or Butterflies.
Artifact Curator (Silver): Find and collect all of the Artifacts.
Memento Specialist (Silver): Collect all of Carl's Mementos.
Environment Badge (Silver): Break apart at least 500 objects.
Adventure is Here (Gold): Defeat Muntz's canine squadron in the skies above Paradise Falls.
Merit Badge Champion (Gold): Collect 6000 Merit Badges in the game to become the Merit Badge Champion.
Multiplayer Extras (Gold): Unlock the extra Multiplayer Combat Maps.
Ellie Badge (Gold): Complete all of the Quest Cards for a special badge.
Platinum Trophy (Platinum): Unlock every Trophy in the game.

Additionally, there are three secret trophies:

Secret trophy (none): Unknown.
Secret trophy (none): Unknown.
Secret trophy (none): Unknown.