Unlock Ziggy Swimsuit Costume:
Complete the Advanced Hakox levels.

Unlock Allen Swimsuit and Chaos Flawless Costumes:
Complete and save the game then load the cleared saved game file.

Unlock JR's Swimsuit Costume:
Go to the south eastern section of the map and at the main street look for a small side street and head east and you will find the treasure chest that contains the armour for JR that changes his character model.

When you can move around in Miltia's map go as far to the right as you can and on top of a building you will see a treasure chest. Select the treasure chest and enter the code 5150 when prompted.

To begin with Shion's Vector costume from Xenosaga: Episode 2 start a new game and then load a completed saved game file from Xenosaga: Episode 2 on your Memory Card.

Successfully beat the game once to unlock Swimsuit mode in the Memory Code event viewer.