To Find is to Lose
After the opening scene you receive the Traverse Town World Card. You'll be forced to use it here on the first floor. You'll start the tutorial on the combat system and once it ends you'll receive the Key of Beginnings . Another tutorial takes over where you'll smash a barrel to acquire a Blizzard 5 and be thrown into battle with some Shadows.
Afterwards, break the barrels and crates as well as street posts to release HP balls and MP balls. Approach the door and use the card you acquired from defeating the Shadows to create a new room. If you need to take a break use the Moment's Reprieve, else use your other card. Move up to the next room and use the Key of Beginnings to enter the room to the left. Here you'll meet Leon and another tutorial takes over.
To Lose is to Find
After the tutorial you'll receive Simba and the Key of Guidance . To reach the next room you'll need a 3+ map card to enter, so you'll likely have to fight some Heartless to get one. Clear out the next room you make and enter the Room of Guidance using a 3+ and the Key of Guidance card. After the scene you receive the Key of Truth . Head to the next room, it requires a 9+ card to enter, but remember that 0 cards meet all criteria. Clear this room then enter the Room to Truth using a Green Card and the Key to Truth. You'll want to make sure you've reached level 7 for this fight to get the Stun Impact sleight.
BOSS - Guard Armor
Being the first boss in the game, the Guard Armor is relatively simple. You have to defeat the arms and legs before attacking the body, but with some cards above 5, you should be able to slash endlessly. Remember to combine your lower level cards so they don't get broken, and wait on using your Potion until your reload counter reaches 3. The Gimmick Card in this fight can be used to make the Guard Armor crumple into a heap of it's parts. It shouldn't be hard to break at least one part with this useless card. If you are still struggling, wait for some Donald or Goofy cards to drop. Use them in a sleight to get the most out of your deck and deal a lot of damage. Once defeated it drops Guard Armor Enemy Card.
Got it Memorized?
After the fight you'll be in the Conqueror's Respite. You can go down a room if you want to create one, but make sure you save, then exit back to Castle Oblivion. Here you'll meet Axel who immediately challenges Sora!
BOSS - Axel
Axel wields flaming chakrams and won't hesitate to throw them at you. Luckily this particular attack is easy to dodge, or you can just card break it. If you are up close, Axel will use a three hit combo that can deal some damage, but again you can always card break this. As Axel begins to stock cards up for a sleight, be ready to use a 0 card. He will use Fire Wall if you don't break the sleight, it can be damaging and difficult to avoid. Overall the fight shouldn't be too tough, heal when you need to and reload when you have some space. He drops Fire when defeated.
More Worlds to Visit
You will receive five more World Cards and the order you go to them definitely matters. The floor layout will always be the same for the floor you are on, regardless of which world you enter. The thing that changes per floor is how strong the enemies are, including the Bosses.