Here is the full list of all 27 Run Rabbit Run achievements.
Past 10 levels in green time
Collect 100k score since the beginning of the game
Past 5 levels in green time
Make a 1000 jumps since the beginning of the game
Make a 5000 jumps since the beginning of the game
100 deaths since the beginning of the game
500 deaths since the beginning of the game
1000 death since the beginning of the game
5000 death since the beginning of the game
50 deaths since the beginning of the level
100 deaths since the beginning of the level
300 deaths since the beginning of the level
Collect 500k score since the beginning of the game
Collect the biggest carrot and open the second chapter
Past 20 level in green time
WOW, past 35 levels on green time
10 deaths from trains
50 deaths from spikes
300 jump on jumpads
50 death from the rocketlaunchers
Kill 300 birds
Collect all carrots in 10 levels
Collect all carrots in 18 levels
Collect all carrots in 32 levels
Collect all carrots in all levels
10000 deaths since the beginning of the game
1000 deaths since the beginning of the level