To obtain the strongest equipment in the game you must have all the Doppleganger items from Volume 1 and Volume 2 and defeat Doppleganger two times in Volume 3. After the second time you defeat him, he will drop the armor "Other Self" and the accessory "Shadow" which are level 150, but the best items in the game.
Easy first place steam bike race
When attempting the steam bike missions, when you are about to tag a King Chim Chim press Select then press Circle. If done correctly, you will either get three King Chim Chim or finish the race which will give you an easy first place.
Forest Of Pain
Defeat Cubia to complete the game. After the credits you will be able to access the Forest Of Pain.
Invincible Zelkova
Obtain the armor customization item Indulgence which takes damage and converts it to GP damage. Give it to Zelkova. He will not take most damage because he has 99,999,99 GP.
Natsume
To unlock Natsume, head to the BBS after eliminating all of the Chaotic PKs. If you then go to any area in the game, you will find her in a Battle Zone.
Tabby
To unlock Tabby, access the Forest of Pain's fiftieth floor.