LEGO Batman

This Achievement is easily gained, whether you are playing with a friend or on your own.

When playing with a friend, both characters must be linked to separate controllers while you are still in the Batcave/Arkham Asylum. Start and finish any mission (Story or Freeplay) with your friend. Assuming you are both signed in to different Gamer Tags, you will both get the Achievement.

If you are playing on your own, you can mimic the above scenario by turning on a second controller (or any peripheral with a D-pad and face buttons) and making sure that both characters are linked to separate controllers before starting the level (again, in Story or Freeplay). You can have one Gamer Tag signed in, or sign in as another one if you feel it is needed.

As long as both characters are being controlled at the beginning through to the end of any level, you will get this Achievement.

After trying it, i found that if you do this alone it's easier to do on Arkham Bonus level because you just have to get studs to finish the level,

Doesn't have co-op jumps, opening doors, just hop on some car/robot with both controllers, and simply get studs with one.

Simple as that.

Just complete the first level with a friend. Enter co-op in the batcave though as the whole mission has to be done before the achievement unlocks. If you are short a controller and/or a friend, you can use the Guitar Hero guitar. it just takes a bit longer

While in the batcave set up a second controller, either by yourself or with a friend. As z0rrofox mentioned you can use a guitar hero controller if you need to (or a joystick or a whatever). You should then complete a level, in either story mode, and the achievement should pop upon completion.

Some tips:
It's easier to do this with a second person because you can only move as long as both people are moving with the screen.
It's easier to do this with a second person because the game is made for teamwork.
The first levels are obviously going to be the easiest.