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