Remember that you don't have to wait until the end of a sequence (such as an investigation sequence or a part of a trial) to save your game. You can save your game, quite literally, at any time by simply pressing the Start button. This will bring you to the menu where your game can be saved. After saving, you'll be brought back to the start menu.
There are five cases total in this game. To unlock cases, you must successfully complete the case before it. Once a case is unlocked, however, you can go back to it and replay it at any time.
To unlock all of the cases in the game instantaneously, insert your Gyakuten Saiban (Phoenix Wright in Japan) GBA cartridge into your Nintendo DS GBA slot.