Supermoves are done by pressing + at the same time with a full super meter. This achievement can be unlocked using the games training mode. From the main menu select Singleplayer -> Training -> Practice.
Select two characters, and any stage.
As soon as it's loaded, hit START and navigate to PRACTICE OPTIONS. Find SUPER METER and change this option to FULL.
Hit + to perform the characters supermove. Once the animation ends, go to PRACTICE OPTIONS again and change CONTROL PLAYER to 2 and do the supermove for the other character.
After that, hit START and choose PLAYER SELECT. Repeat these steps for each of the games 24 characters and the achievement will unlock.
You can do this practice mode. After starting practice, press start and go to practice options, set the super meter to "full". Perform the super move (there are 24 characters, each character has one super move) and return to player select. Select the next fighter and keep going. Super Moves can be triggered by pressing LT+RT.