Here is the full list of all 28 Zool Redimensioned achievements.
Perform a Heavy Spin Attack
Smash through a hidden wall
Clear one level in either mode
Do a push-up
Complete Ultimate Ninja Mode
Launch the 1992 original
Complete Redimensioned Mode
Take out The Hum-Bug
Take out Jimmy Guitar
Take out Bananaman Sam
Take out The G.D.K.
Take out MAX-3 the Robot
Take out The Gaffer
Take out the Kactus of Krool
Complete both Redimensioned and Ultimate Ninja Mode
Hit a cymbal with a projectile that has bounced off a drum
Find the secret in Music World
Hit three enemies with one sliding kick
Collect all the big collectibles in Redimensioned Mode
Beat a developer speedrun record
Use a strength tester to boost your jump
Complete 1-4 without touching the treacle
Pull a radish and slice a carrot in the same level
Defeat the boss of any world without killing any other beasties
Find the one collectible
Collect all the big collectibles in Ultimate Ninja Mode
Successfully complete a secret level
Find a secret level