Apophis, Skullfeather First Form, Skullfeather Final Form fully pwned:

Defeating an anachrony is the main thing, it gives the main rewards (like eternal daphnes).  But there are sub-challenges with sub-rewards, that are more difficult than the main task.  The biggest challenge is defeating the anachronies without the use of dream tears, which buff your stats temporarily for that anachrony fight.  There are other challenges though, like using particular characters.  Every anachrony has three challenges in all, and I've now defeated all of these challenges as well as all of the anachronies.

I'm the undisputed master of the game.  I've beaten everything they've thrown at me.  It only cost thousands of dollars to do so!  I sure showed them!

Honestly, the 3.0 game changes made these fights easier.  The two additional uses of exclusive skills across the board were really helpful.  The fact that Megumi's master skill, Psychic Charge, went from giving +2 sp to +6 sp is crazy helpful.  I was already happy with its +2 sp version.  The fact that you can use overdrive whenever you want, not just when it's exactly at 100% full, is really convenient.  By this I mean if you activated overdrive in the past, and your bar was at say 150% full, you'd just lose that 50%.  But now your overdrive bar goes from 150% to 50%, so you're well on your way to your next overdrive.  That is a huge benefit.

I'm proud I defeated Skullfeather before these 3.0 changes occurred.  I beat the real, old-school, god-difficulty tier Skullfeather.  New players of the game can't even understand what I managed to do.  That old Skullfeather was much tougher than this new, 3.0, Skullfeather Final Form.

I also acquired fireworks Miya limit break level 3 and belly dancer Vritika level 1 due to some lucky free rolls.  Fireworks Miya is so niche she's basically useless, so it's annoying I keep getting her.  Belly dancer Vritika has the potential to be strong, but currently she's weaker than my base version of Vritika, which is limit break level 4, so I can't use her either.  I don't actually need to get stronger though, I just beat all the bonus difficulty challenges of the toughest bosses in the game.  >.<.

Thanks to beating all those anachronies, some of my characters have reached title badge level 8.  They get a new skill slot if they can reach level 10, but that still seems to be a distant prospect.  Even my weakest characters are at a respectable title badge level 6 now, because I had them hide in the back ranks and get credit for defeating all these anachronies while the frontline squads did all the work.