LEGO Batman

Go to free play as penguin and a second controller as a SWAT cop and just kill the cop 20 times with the penguin bomb.

Do the First Mission of the Second Episode. First off, this can be done DURING Story Mode, meaning you don't have to leave and reload.

Blow up the gate immediately to your right and run down the ramp. A small cut scene begin, and then you will be left with 5 police officers. These should be your first 5 (if you don't get all 5 with bombs, you will have infinite tries in a bit). After this, use Bane and toss the truck trailer out of your way. Leave the truck, as it is not important now. Head forward a small distance and turn right, going all the way to the fence. This is your spot for getting easy kills. Officers will spawn above you on the stairs and right below and to the left of the stairs and run towards you. You can do this 2 ways:

1.) Release a penguin aimed at an officer. The blast should eliminate several in the direct vicinity.
2.) Release a bomb in the general direction of the officers and hold B to explode it manually.

I did a mixture of the 2; method 2 for large groups, and when there were 1 or 2 remaining, I would get next to them and release the bomb, exploding on contact. Do note that this requires Invincibility if you would like to keep your studs you have gained thus far.

Repeat this process until you get the 20 kills (give the game a second or 2 to pop the achievement) and continue with the level!

Go to the Villain Campaign and play any misson on free play and on the character screen choose the Penguin.
Once you start the mission press Y to control the 2nd character and change it to POLICE OFFICER. Now press Y again to control Penguin and press B to use a mini penguin bomb. Once you hit the 2nd character it will die.
Do it 20x and the achievement will unlock - I did it this way.