A quick translation from someone over on the Disgaea 3 boards at GameFAQs. It seems like some of these will be challenging and none have to do with the main storyline at all! Looking at it more closely, you could probably achieve all of this without having to restart the game completely over.
Gold
- Clear LoC Item World from floor 1 to 100 without exiting.
- During Reverse Pirating, collect all innocents, treasures, and level spheres on the map
- Deal 10 billion damage
Silver
- Find the Trophy Room in 90+ Item World
- Defeat Prinny Pirates
- Defeat Diez Gents Pirates
- Defeat Ball Pirates
- During Reverse Pirating, collect all innocents
Bronze
- Clear Item World from floor 1 to 100 without exiting.
- There are 21 bronze trophies for defeating each pirate.
- In Item World's Tower room, speak with the Cat at the top.
- During Reverse Pirating, collect all treasures
- Deal 100 million damage
- Deal 1 million damage
- Perform 9 counters in a row
- Achieve 5 color chains with geopanels
- Play for a 10 hours session
- Defeat an unit in battle with a 10-hit combo
- Perform 100 jumps
- Defeat an unit in battle with a 10-unit tower attack
- Find Akutare/Axel in the Item World
- Pass a homeroom proposal by force
- Achieve 255 turn stationary bonus.
- Capture an enemy
- Perform 5 magichanges in battle