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