There's a lot of content in Lightning Returns: Final Fantasy XIII, all of which we cover in the official game guide. Today, it's all about farming bosses to obtain valuable Components.

On Hard Mode, main quest bosses drop top-tier Components in high quantities. By rushing straight to them and restarting new playthroughs via the Crystal of Atonement, you can actually defeat some of them repeatedly in very little time. 

  • Noel: You can reach Noel very quickly. Complete chapters 1-1 and 1-2 on the evening of Day 1, then sleep at the North Station inn until 00:00 on Day 2. Sprint to the phone booth without bothering with the codes, enter any four digits, then fight the Dreadnought that appears to open the gate. You can then run to the Graveyard monument, and finally to Noel in the Warren in mere minutes. Defeating him rewards you with the rare Tornado spell, 30 guaranteed Holy Forgefire items, and one to three guaranteed Crystal Malistones if you equip the Beggar’s Beads.
  • Caius: Assuming you have extra chocobo healing items from a previous playthrough (which should be the case if you follow the Complete Official Guide’s recommendations), saving and healing the chocobo takes only a few minutes. You can then head straight to the Temple of the Goddess and defeat Caius to obtain the rare Flare spell, 30 guaranteed Demonic Forgefire items, and one to three guaranteed Crystal Malistones if you equip the Beggar’s Beads.

Now read this feature covering Abilities & Synthesis in Lightning Returns.