Here is the full list of all 25 Purple Heart achievements.
Swim in the water
Go down to level 3
Learn to make a dash
Grab coin
Push the box
Start the game
Finish 12th level
Find a big gun
Finish half of the game
Kill first enemy
Finish the game
Find a jetpack
Complete 13 level
Pass level with a large saw
Complete 8 level
Complete 14 level
Unexpected meeting
Complete 4th level
Meet the robots
Complete 15 level
Complete 16 level
Find a machine gun
Find a gun
Complete 10th level
Complete 1st level