After obtaining all paradox endings and 160 Fragments, a secret paradox ending, "A World Without a Goddess," plays after the end credits. This only happens if you collect all the Final Fantasy 13-2 Fragments in which below you can see all the locations of each. All the fragments can be located in all the 10 wild artefacts locations through out the Historia Crux.
Need additional help on locations, walkthrough and guide then see links below:
Final Fantasy 13-2 Walkthrough
Final Fantasy 13-2 Guides
Final Fantasy 13-2 Wild Artefacts Locations
New Bodhum -003 AF-
Gogmagog Fragment Alpha (Story)
Gogmagog Fragment Beta (Story)
Heart Prism (Side Quest)
Graviton Core Alpha (Story/Collection)
New Bodhum – 700 AF –
Cartesian Board (Hidden Item)
Laplacian Board (Hidden Item)
Hope’s Message (Treasure Cube)
Noel’s Message (Alternative History)
Serah’s Message (Alternative History)
New Bodhum – Year Unknown –
Vanille’s Fruit (Treasure Cube)
Fang’s Crown (Treasure Cube)
Transcript: Fate and Freedom (Paradox Ending)
New Bodhum – ??? AF –
Transcript: Beneath a Timeless Sky (Paradox Ending)
Bresha Ruins – 005 AF-
Atlas Fragment (Story)
Ghast Fragment (Side Quest)
Delicate Crystal
Vita Lyrica
Anima Miseria
Unio Mystica
Ars Symphonica
Graviton Core Beta (Story/Collection)
Bresha Ruins – 100 AF –
Kalavinka Fragment (Side Quest)
Ruthenium Ring (Side Quest)
Rhodium Ring (Side Quest)
Palladium Ring (Side Quest)
Osmium Ring (Side Quest)
Adamantite Ring (Side Quest)
Bresha Ruins -300 AF-
Control Device Password 2 (Side Quest)
Iridium Ring (Side Quest)
Platinum Ring (Side Quest)
Mythril Ring (Side Quest)
Yaschas Massif -010 AF-
Aloeidai Fragment (Story)
Pathos Jewel (Side Quest)
Misery’s Bead (Side Quest)
Amur’s Sphere (Side Quest)
Innocence’s Sacred Sphere (Side Quest)
Yaschas Massif -01X AF-
Gorgyra Fragment (Side Quest)
Orb of Clotho
Sword of Lachesis
Mirror of Atropos
Yaschas Massif – 100 AF –
Schwertleite’s Flower (Side Quest)
Helmwige’s Nightshade (Side Quest)
Siegrune’s Spiritbloom (Side Quest)
Rossweisse Skyblossom (Side Quest)
Book of Shambala (Side Quest)
Book of Valhalla (Side Quest)
Graviton Core Epsilon (Story/Collection)
Yaschas Massif -110 AF-
Control Device Password 1 (Side Quest)
Ugallu Fragment (Side Quest)
Waltraute’s Flower (Side Quest)
Gerhilde’s Blossom (Side Quest)
Ortlinde’s Bloom (Side Quest)
Book of Avalon (Side Quest)
Oerba -200 AF-
Time’s Stardust
Time’s Shell
Time’s Coral
Giant Egg (Collectable)
Graviton Core Gamma (Story/Collection)
Oerba -300 AF-
Spinning Moonstone (Temporal Rift)
Sparkling Runestone (Temporal Rift)
Astonishing Limestone (Temporal Rift)
Thrilling Milestone (Temporal Rift)
Lovely Starstone (Temporal Rift)
Bubbly Stone (Temporal Rift)
Scorching Firestone (Temporal Rift)
Dewy Bloodstone (Temporal Rift)
Mossy Rosetta Stone (Temporal Rift)
Oerba -400 AF-
Bittersweet Chiffon (Temporal Rift)
Temulous Muffin (Temporal Rift)
Beloved Cinnamon (Treasure Cube)
Selfish Pancake (Temporal Rift)
Farewell Madeleine (Temporal Rift)
Teatime Mont Blanc (Temporal Rift)
Dishonest Mille-feuille (Temporal Rift)
Pink Parfait (Temporal Rift)
Graviton Core Zeta (Story/Collection)
Oerba – ??? AF –
Transcript: Vanille’s Truth (Paradox Ending)
Sunleth Waterscape -300 AF-
Mutantomato Fragment (Story)
Extraordinary Egg
Sunleth Waterscape – 400 AF –
Miniflan Fragment (Side Quest)
Lapis Lazuli (Side Quest)
Heliodor Ore (Side Quest)
Carnelian (Side Quest)
Celestine (Side Quest)
Cosmo Aura (Side Quest)
Graviton Core Eta (Story/Collection)
Sunleth Waterscape -??? AF-
Transcript: Mog’s Marvellous Flan Plan (Paradox Ending)
Coliseum – Year Unknown –
White Hole Gem (Story)
The Archyite Steppe – Year Unknown –
Black Hole Gem (Story)
Goblin Fragment (Story)
Fragment of Invincibility (Side Quest)
Ochu Fragment (Side Quest)
Long Gui Fragment (Kill Long Gui)
Yomi Fragment (Side Quest)
Woolly Stone (Story)
Crimson Crystal (Side Quest)
Azure Crystal (Side Quest)
Forest Crystal (Side Quest)
Amber Crystal (Side Quest)
Violet Crystal (Side Quest)
The Archyite Steppe – ??? AF –
Transcript: A Giant Mistake (Paradox Ending)
Serendipity –Year Unkown-
Chaos Crystal (Prize)
Setzer’s Dice (Prize)
Chocochick Down (Collectable)
Fragment Name Here
Priceless Gift (Prize)
Academia -400 AF-
Zenobia Fragment (Story)
Academic Rank: Paradox Professor
Travel Guide: New Bodhum
Travel Guide: Bresha Ruins
Travel Guide: Massif
Travel Guide: Oerba
Travel Guide: Sunleth Waterscape
Travel Guide: Academia
Travel Guide: Augusta Tower
Travel Guide: Vile Peaks
Travel Guide: Archylte Steppe
Travel Guide: A Dying World
Graviton Core Delta (Story/Collectable)
Academia -4XX AF-
Academic Rank: Monster Professor
Quiz Rank: Private (Answering Amodar’s Questions)
Quiz Rank: Sergeant (Answering Amodar’s Questions)
Quiz Rank: Lieutenant (Answering Amodar’s Questions)
Quiz Rank: Colonel (Answering Amodar’s Questions)
Quiz Rank: General (Answering Amodar’s Questions)
Stoic Virtue (Finishing Brain Blast Terminal)
Epicurean Song (Finishing Brain Blast Terminal)
Lyceum Knowledge (Finishing Brain Blast Terminal)
Academia Wisdom (Finishing Brain Blast Terminal)
Transcript: The Future is Hope (Paradox Ending)
Academia – 500 AF –
Paradox Scope (End Boss)
Amethyst and Luvulite (Story)
Augusta Tower – 200 AF –
Proto Fal’Cie Adam Fragment (Story)
Idea Circuit (Side Quest)
Enigma Codex (Side Quest)
Difference Engine (Side Quest)
Augusta Tower -300 AF-
Entropy Board (Story)
Augusta Tower – ??? AF –
Transcript: Test Subjects (Paradox Ending)
Vile Peaks -010 AF-
Twilight Fragment Alpha (Side Quest)
Baxter’s Last Light (Collectable)
Ray’s Last Light (Side Quest)
Sarge’s Last Light (Side Quest)
Vile Peaks – 200 AF –
Falcon’s Compass (Side Quest)
Twilight Fragment Beta (Side Quest)
Torreno’s Last Night (Side Quest)
Falcon’s Last Light (Side Quest)
Thunder’s Last Light (Side Quest)
Blitz Squadron Mission Report (Side Quest)
Words of Light (Side Quest)
Father’s Song (Side Quest)
A Dying World – 700 AF –
Gogmagog Fragment Gamma (Story)
Ultima Brand (Hidden Treasure Cube)
Omega Brand (Treasure Cube)
Chaos Brand (Hidden Treasure Cube)
A Dying World – ??? AF –
Transcript: Heir to Chaos
The Void Beyond – Year Unknown –
Etro’s Sorrow (Story)
Pulse’s Resolution (Story)
Lindzei’s Desire (Story)
Mwynn’s Tenderness (Story)
Bhunivelze’s Sleep (Story)