Kingdom Hearts 0.2 is a short, linear game that takes place in the Dark World, with the subsequent areas representing the worlds of Birth by Sleep (Castle of Dreams based on Cinderella, Dwarf Woodlands based on Snow White, and Enchanted Dominion based on Sleeping Beauty) that have fallen to the darkness. As such, these worlds have taken on sinister appearances, and have been invaded by a plethora of new enemies.
Before beginning the game, you must choose a difficulty. Beating the game on Proud (which is the hardest difficulty available by default) or Critical (which must be unlocked by beating the game) will count toward an achievement/trophy, and beating the game on Critical is necessary for an objective that unlocks upon starting a subsequent playthrough. After the tutorial (which you can skip at any time), proceed forward until you come across your first battle. This is against Shadows, the weakest type of Heartless, so it should be completed relatively easily even on Critical. These Shadows also count toward Objective #1: Defeat the Shadows. Collect the HP that they drop if needed, and continue on toward the castle after the scene. After another scene, walk forward and Aqua will hop across the rocks and slide across the icy trail. In the center of the path ahead is a chest containing a Potion, which can be accessed via the item command in the command menu. After defeating another group of Shadows, proceed to the next area. This will trigger a scene and an achievement/trophy.