Here is the full list of all 39 Rad Rodgers achievements.
Complete W1L1
Find the Excalibat
Find a Secret Area
Skip a cutscene
Defeat Mother Nature in 4 minutes
Collect a Lion Trophy
Collect all Lion Trophies
Complete W1L1 100%
Complete W1L2 100%
Complete W1L3 100%
Complete W1L5 100%
Complete W1L6 100%
Complete W1L9 100%
Complete Jungle World 100% on Normal mode
Find the Dopefish
Find all Secret Areas
Watch all the credits
Complete a level without dying
Dusty Slam every kind of enemy
Complete a level without killing a single enemy.
Complete and kill all enemies in a level only using Dusty Slam
Drown 5 times
Kill every single enemy in the entire game, no enemies left alive
Push 5 enemies to their deaths
Collect all Gems in the game
Visit all huts
Complete W1L7 100%
Complete Jungle World 100% on Hard Mode
Complete Jungle World 100% on Easy Mode
Complete W1L4 100%
Complete W1L8 100%
Defeat the first Boomer in less than 30 seconds
Defeat the second Boomer in less than 30 seconds
Use the Photo Mode
Find all Hats
Unlock all Artwork
Complete Pogo Vertigo 1 100%
Complete Pogo Vertigo 2 100%
Complete Pogo Vertigo 3 100%