Here is the full list of all 14 Zuma's Revenge! achievements.
Complete Adventure Mode
Acquire an 11x Multiplier Bonus in Challenge Mode
Beat Ace Time on 10 unique levels
Hit a Double Gap Shot
Get a 20x Chain
Trigger a powerup by using the Laser, Lightning or Tri-Shot
Acquire 8 fruits using the Proximity Bomb
Win an Ace trophy in 4 Challenge Cups
Earn at least 25,000 points from a Multiplier Bonus in Challenge Mode
Force feed the God of Pestilence 20 balls in 20 seconds
Beat Heroic Frog Mode
Get two Clear Curve Bonuses on one level
Beat Iron Frog in less than 25 minutes
Activate MuMu mode