There are 32 Bronze Trophies, 5 Silver Trophies, 4 Gold Trophies, and 1 Platinum Trophy for this title.

Bronze:

A Bird Named Kevin
Objective: Find Kevin before Muntz does.

A Voice In The Mist
Objective: Find the voice in the mist.

Adventure is Out There
Objective: Defeat the first wave of combat planes.

Animation Badge
Objective: Unlock the Bonus Art.

Bird Watching Badge
Objective: Locate Kevin for the first time.

Buddy System Badge
Objective: Free your buddy from five Snare Traps.

Defense Badge
Objective: Successfully defend against 10 dog ambushes.

Entomology Badge
Objective: Collect all varieties of each Butterfly and Dio Bug in the game.

Excavation Badge
Objective: You've found the hidden cave in "A Voice in the Mist."

First Aid Badge
Objective: Use Russell's Canteen three times.

Fishing Badge
Objective: Survive against the hungry Piranhas.

Hiking Badge
Objective: Find the picture-perfect view of Paradise Falls.

Karate Badge
Objective: Break open 10 watermelons.

Kite Badge
Objective: Use Carl's House to float across all the chasms in the game.

Knot Tying Badge
Objective: Tie off the house so it doesn't float away.

Meet the Pack
Objective: Meet the pack: Alpha, Beta, and Gamma.

Music Badge
Objective: Use Russell's Bugle three times.

Night in the Jungle
Objective: Avoid being captured by Muntz's dogs.

Paradise Falls
Objective: Help Carl get his house to the top of Paradise Falls.

Pest Control Badge
Objective: Squish 10 Wasps and Spiders.

Rare Statue Badge
Objective: Find and collect the Gold Jaguar.

Recycling Badge
Objective: Play through any previously completed level in Story Mode.

Sharp Tools Badge
Objective: Use Russell's key to cut through three items in the game.

Shoveling Badge
Objective: Dig up all of the hidden bones using Dug.

Sinkhole Terror
Objective: Defeat the giant Crocodile.

Slide and Slither
Objective: Defeat the giant Anaconda.

Spirit of Adventure
Objective: Free Russell and Kevin, then escape the Dirigible.

Survivor Badge
Objective: Complete any Story Mode level without failing or quitting.

Swimming Badge
Objective: Swim through all of the areas that have water.

Teamwork Badge
Objective: Defeat either the giant Anaconda or Crocodile with 2 players.

To Paradise Falls
Objective: Complete the level to start Carl's journey to Paradise Falls.

Wings Badge
Objective: Defeat the first plane in the battle...