Following all the opening cinemas and dialogue, you will have the opportunity to enter your first world, Traverse Town. As in the original Kingdom Hearts, this is the current residence of Final Fantasy mainstays Leon, Yuffie, Aerith and Cid, and in Chain of Memories it serves as a kind of tutorial to illustrate exactly how the card-based combat system works. As such, it really isn't too difficult on the whole. Near the end of the level, after you unlock the door with the Key to Truth card, you'll square off against a familiar boss, the Guard Armor that also terrorized Traverse Town in the original Kingdom Hearts. This isn't too hard of a fight on the whole, so long as you make good use of the 0-strength Mickey Silhouette cards that appear during the battle. Use them to counter one of the Guard Armor's attacks and it'll leave him paralyzed for a short time, allowing you to move in and pound away with your attack cards. The Slide Dash Sleight can help early on as you work to take out his legs, but don't overuse them since they can eat away at your deck. I took him out rather easily at Level 6. Beating the Guard Armor will net you his card for use in future battles.
Once you finish him off, make sure you save before exiting Traverse Town, because there's another boss fight waiting right around the corner. Go back and change up some of the rooms if you feel the need to battle more Heartless and gain a few additional levels. Once you're ready, exit through the door back into Castle Oblivion and prepare to face Axel in the first of what will be several fights against Organization XIII. This is a tougher fight than the Guard Armor one was, but it still isn't all that hard. Beware his Firewall slight when he uses it, because it can cause some massive damage if you're not careful. The Pluto cards you get here can be a big help, as Mickey's canine pal can dig up some immensely helpful healing spheres. Slide Dash works well here, especially if you can use it to Card Break Axel's Sleights, but again make sure you don't overuse it. Afterwards, you are rewarded with five additional world cards -- Agrabah, Olympus Coliseum, Wonderland, Monstro and Halloween Town. Agrabah is the one that appears right next to Traverse Town on the World Cards screen and is also the first one that appears when you hit the triangle button in front of the door, we'll choose that as our next destination.