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