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