Here is the full list of all 29 Rabbit Island achievements.
Complete episode 1
Complete episode 2
Complete episode 3
Complete episode 4
Complete episode 5
Complete episode 6
Complete episode 7
Complete episode 8
Complete episode 9
Complete episode 10
Complete the episode and save 60 carrots
Save 600 carrots
Set one improvement on tower
Sell improvement on tower
Open all towers
Improve all towers to the max
Improve one type of rabbits to the max
Improve all types of rabbits to the max
Improve one type of perks to the max
Improve all types of perks to the max
Win the "towers vs towers" game 3 times in a row
Play the "towers vs towers" game 20 times
Win the "towers vs towers" game 10 times
Lose the "towers vs towers" game 10 time
Play the "towers vs towers" game on all maps
Beat a higher-level player in the "towers vs towers" game
Win any game with none of your towers in the field in the end
Collect 1000 coins
Improve towers, rabbits and perks to the max