This seems like quite a daunting achievement, but don't be intimidated. Head Chomper can easily be done in level 2-1 [the first stage in Russia].
You will start out on the ground being prodded by KGB agents, and then you will get up and can start the level. Go through the level until you reach the very first watch tower, then go further and you will see a sort of lump of snow that allows you to stand on one side of it without being shot at. Go to the NEXT lump of snow where you can stand without being shot from the other side of it.
Now, there should be 4 agents ready for head chomping available to you!
I recommend getting a piece of paper and a pencil so you can make tally marks. To help you get the pressure off of yourself try and take a break a small pause break after 10, 20, or even 25.
What I did that helped me was after every single head chomp I paused the game, marked the tally down, and then un paused it by pressing START. DO NOT PRESS A TO UNPAUSE THE GAME!! Occasionally the game will register this as a jump, so you definitely don't want to press A since you could easily lose the agent you're on the head of ;]
Use this YouTube video to help you find the place I'm talking about. Good luck!