Here is the full list of all 11 Bubsy: The Woolies Strike Back achievements.
Unlock the Wooly Vault in every Level
Defeat the Twin Empresses Poly and Esther
Obtain all T-Shirts in the Final Region
Beat every Level without losing a single life
Accumulate a total high score of 600.000 points
Defeat the Gunslinger UFO
Obtain all T-Shirts in the Desert Region
Accumulate a total high score of 400.000 points
Obtain all T-Shirts in the Mountain Region
Defeat the Tentacle UFO
Accumulate a total high score of 200.000 points