The first Emerald computer is story mission.
The first Amethyst computer is in a funny spot. Enter the 1st Olict Space. Instead of taking the mirror at the top of the stage to proceed, go as far left then south as you can. You'll enter the Olict Space version of the lobby. The first computer is through the stairs at the top right of the stage, leave the Olict Space through the mirror in the basement.
For the second Emerald computer, go to the room with Doll challenge. At the bottom of the stage, just past her, is a mirror. Take it, then go south into the next stage. Follow the top to get to the Olict Space main stage, and follow the wall to go south again. Stairs on the left top of that stage lead to Emerald's second computer after leaving olict space through the mirror in the basement.
For the final Amethyst computer, go out the far left and south exit from the Doll. It's through the door on the left side.
Once you've erased all the data, you need to return to base and get it removed by the Goth Loli Knight. If you fight a camera olict and it takes a picture of you, you have to erase the data again. Normal photos are the first computer, climax photos are the second computer. Avoiding combat is your best option between computers 1 and 2, and then use a Return Ticket.