Here is the full list of all 28 Zool Redimensioned achievements.
Complete Redimensioned Mode
Take out the Kactus of Krool
Take out The Gaffer
Find a secret level
Take out MAX-3 the Robot
Take out The G.D.K.
Take out Bananaman Sam
Take out Jimmy Guitar
Find the one collectible
Take out The Hum-Bug
Smash through a hidden wall
Launch the 1992 original
Clear one level in either mode
Perform a Heavy Spin Attack
Complete Ultimate Ninja Mode
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
Do a push-up
Collect all the big collectibles in Ultimate Ninja Mode
Successfully complete a secret level