Credit goes to Avaritia Aurous for new method.
For this achievement, it asks you to play every starting character (excluding secret and DLC characters).
There are two ways to get this: You can finish the stage with the character you have selected. Or alternatively, you can unlock it in a quickest way by simply play as any character (can be done in any order), wait until the stage loads, then press start and quit out. Repeat this until the achievement pops.