If you missed anything on your way through the story mode, such as Map Events or the alternate endings, you aren’t out of luck. You always have the option to abuse the space-time continuum for your own twisted needs.
You may have noticed a doorway in Laharl’s throne room before now, across from his bedroom, which looks like it should go somewhere but doesn’t. In the Post-Game, that’s where the Time Traveler has set up shop. At any time in the Post-Game, you can speak to the Time Traveler to be returned to the start of the game.
You’ll reappear in Laharl’s throne room, ready to go through the story mode all over again. Your equipment, levels, Customer Rank, achievement progress, and training at the Demon’s Dojo all survive the trip into the past without alteration. The Time Traveler himself does not.
There are a few changes, naturally. Sicily, Lanzarote, Barbara, and all other unique characters you’ve recruited will leave your roster at the start of a new cycle. They will reappear as you work your way back through the missions where they were recruited, and rejoin your team just as they did in your previous cycle, at the same level and using the same equipment as before. (That is, if Sicily was level 90 when you opted to start a new cycle, she’ll be level 12 when you fight her at the end of Episode 2 and will then suddenly be level 90 again at the start of Episode 3. Time travel is fun.)
If either Laharl or Flonne were in their altered forms when you started the new cycle, they both revert to their default forms and Evilities, while Etna’s hair returns to its natural color. Etna does get to keep The Last Majin, however.
Going back in time at least once unlocks the Battle Dialogue cheat in the Cheat Shop, which you can toggle on to remove all Map Events. If you fulfill their requirements, they simply will not occur. If you’re still working on the Battle of Words Trophy, you’ll want to leave that off.