Attack Pattern: Red Koopas fly safely in a back and forth or up and down pattern. They're quite predictable. Green ones bounce all over the ground, and can be difficult to stomp.
Basic Fighting Strategies: A single stomp will remove a Koopa's wings. Green ones require careful timing. A fireball or invincibility will take one out right away.
Advanced Strategies: As with regular Koopas, a grounded Paratroopa can be stomped, and then used as a weapon (go to the Koopa section for more details). You also get more points by doing this.

Attack Pattern: Same as in Super Mario Bros.
Basic Fighting Strategies: Once again, a stomp will cause it to lose it's wings, and a fireball, starman, or hammer will kill it immediately.
Advanced Strategies: You can still use their shells as weapons after knocking them down. You can also use them as stepping-stones across pits in this game. Jump towards one (red are usually the only ones that are worthwhile, as green can't fly over pits), and hold down on A throughout the jump. When you hit the Koopa, you'll do a super-jump which can propel you to a safer place to stand.

Attack Pattern: Green ones bounce around, as in previous games, while red ones are more stable. I believe the blue and yellow ones are more or less the same as red.
Basic Fighting Strategies: Once again, a stomp will cause it to lose it's wings, and a fireball, starman, or a spin-stomp will stop it cold.
Advanced Strategies: You can still use their shells as weapons after knocking them down, and you can use them as stepping-stones again, too. It's a little easier this time, just make sure you hold down on A the whole time you're air-borne, and you'll be able to do a super-stomp off of them.
Also, eating a Paratroopa with Yoshi will have the same results as eating a regular Koopa - extra powers. For more details, see the regular Koopa section.

Attack Pattern: They follow the same basic pattern as in previous games. There are only red and green ones in this game.
Basic Fighting Strategies: If you eat a Para-koopa, they will automatically lose their wings, and you'll hold their shell in your mouth until you spit it out. If you stomp on them, they'll lose their wings and go to regular Koopa behaviour. I believe that a Pound-the-ground attack will kill them immediately, and an egg attack will send them hiding in their shell.
Advanced Strategies: Eat them to get rid of them quickly and efficiently. The shells often make good weapons. Use a pound the ground to beat them completely.

Attack Pattern: All they do is regular attacks, as far as I know.
Basic Fighting Strategies: When you meet them, you'll be all alone with Mario, which limits your strategies to either stomping or regular attacks. It will probably take two regular attacks to knock them down, while a stomp will beat them in one. Even so, you'll want to save some of your FP for the Hammer Bros. battle at the end of the level, so don't stomp them unless you're running low on mushrooms.
Advanced Strategies: You might want to dodge them, as they aren't worth a lot of experience. Still, they aren't that hard to beat. Blocking their attacks can be tricky. They'll charge at you, but then pause for a moment just before attacking...try to hit the A button right at the end of that moment.

Attack Pattern: Paratroopas fly around on the map screen and swoop down on Mario when he gets near. In battle they continue to use their swooping attack to hurt Mario.
Basic Fighting Strategies: On the map, you should Jump on Paratroopas or use the Dizzy Spin if you have the appropriate badge. The Hammer will probably work, but it is hard to time an attack with it. In battle, a Jump Attack, Hammer Throw or POW Block will knock their wings off. After they are on the ground, fight them like normal Koopas.
Advanced Strategies: Use Jump to knock their wings off, anything else is a waste of a good item or FP. Goombario is the best partner to fight these guys with, between his Headbonk and Mario's Jump attack, they can knock all the Paratroopas out of the sky and keep them pinned on their backs. If there are Bob-ombs on the field, Kooper may be a better choice.
When a Paratroopa attacks, it will fly forward, pause, then swoop down towards Mario and bounce off of him. Try to press A just as it hits his body to block. It's often a good idea to let Paratroopas keep their wings for a while, because if you knock them down, enemies that are dangerous to stomp, like Spiked Goomba and Bob-omb, may be protected by the wingless Koopas.