Some fragments can only be unlocked after you've beaten the game. Mainly most Paradox-endings can only be triggered during postgame. Accepting Lightnings offer in Serah's dream and fighting Atlas at full power are the only exceptions. Monster Collector also only works in NG+, as the final boss counts.
Try the bonus bosses at the Steppe, if you think you're strong enough. At Oerba 500 AF is also a bonus boss for you to fight, once you're in postgame. If you have money to spare, try some DLC-Fights or episodes.
Find Captain cryptic at Academia 4XX AF and complete every map to 100 %. Academia and Neo Bodhum won't receive 100 unless Academia 500 and Neo Bodhum are complete, as these places have different map-layouts.