Here is the full list of all 13 Kinaman vs Gray Elephant achievements.
Do not collect any coins on the first level.
Find one secret star at the first level.
Collect 10 coins at a time.
Go through the first level without one death.
Complete the game in "Time Attack" mode.
Complete the training.
Start the game with saving.
To die for the first time.
Start the game with a friend in Splitscreen mode.
Enable cheat mode.
Finish the game completely.
Collect 30 coins at a time.
Go through the first level at twice the speed.