Attack Pattern: On the map screen, Bullet Bills are fired at you by Snifits. You can actually stand on them and ride them across the room, if you time your jump correctly. If a Bullet Bill hits you, you will enter a battle where you must take on Blasters. The Blasters use Bullet Bills for attacking, and also have an attack called "Blazer" which kills one character instantly.
Basic Fighting Strategies: Magic works quite well against them. Regular attacks are not so good - it takes around two or three timed hits to beat each one.
Advanced Strategies: Use Mallow's Thunder attack as soon as possible. It only costs 2 FP, and it will destroy all Blasters immediately. If there is only one Blaster, you may want to just use regular attacks on it, but otherwise, its powerful attacks make it worthwhile to spend the 2 FP.
To block, you basically have to press A as the Bullet Bill hits you. One last thing that's worth mentioning is that Mario's Masher hammer works very well on these enemies.

Attack Pattern: They just sit there and fire Bullet Bills at you on the Map. In battle, they also attack with Bullet Bills, but this makes it hard for you to concentrate your own attacks on the Blasters.
Basic Fighting Strategies: Attack the Bills to minimize damage to yourself, then attack the Blasters between rounds of Bullet Bills. Advanced Strategies: I may add more details later.