Beat the game to unlock the Chaos Flawless costume, the Allen swimsuit, and the ability to access swimsuit mode through the Memory Code event viewer.
Shion's Vector costume:
Have a completed save game from Xenosaga II on your memory card and load it when you start a new game to have Shion wear her old Vector uniform.
Beat the Advanced Hakox levels to unlock Ziggy's Swimsuit.
Thanks to Revolution Readers Falsha and Marcoos!