LEGO Batman

To expand on Lost Raven's solution:

Go to the Batcave and enter CCB199 into the "Enter Code" menu. This will unlock the "Tropical Joker".

Complete the first level to unlock it in Free Play then plug in a second controller and press RB to cycle through the available characters when the level begins. Once you are both the Joker press B to shock the second controller.

Achievement unlocked.

After you unlock the Joker just go into a frre play game and make both of your people the joker walk up to one of them and press B whalla Acheivment Unlocked

This must be done in Free Play

There are two ways to unlock Joker, the first is to actually play the game's story mode, specifically the Villain story.
Joker's story is the third story sector in the Villain campaign and Joker will be unlocked for play by completing the first level.

Alternatively you can use a cheat code to unlock him, the use of the achievement will not effect your achievements so it is fine to use.
Joker (Tropical) - CCB199
The code is entered from the Batcave/Arkham Asylum computer hub.

Once Joker is unlocked for play head to the mission room and start up any Free Play level (That isnt a driving level)
Make sure you pick one of the Joker characters to be in your team.

Once the game begins press / until your character is a Joker, then press to switch to the other player and also switch them to a Joker.

Now with both characters as Joker walk up and press to use the hand buzzer.

Achievement unlocked.
Here's a video showing this.