After you finish the main story, activate the Paradox Scope in Fragment Skills.
Acadamia 4XX for example, with Activate Paradox Scope, pay attention when you handed the Graviton Cores, and after Alyssa handed you the Artifacts, reject the offer. You will get the Paradox Ending.
Same goes to Oerba 200 AF, with Paradox Scope activated, fight Ciaus again. You will get Paradox Ending.
Hope this helps.