Attack Pattern: Some of them are stationary, and some hop around. When you get near, they'll jump, in the hopes of catching you off-guard. Some can also spit fireballs - they point straigt up, and spit them in an arc.
Basic Fighting Strategies: Use any weapon but a stomp, and you should be able to beat them. Stomping would be very bad, since they like to take a bite out of your bottom when you're above them. With the fiery ones, they have a lot of range. Fireballs and hammers work great if you have them, but otherwise you may just want to try and get past them while they aren't spitting, because they have a pretty good aim - it's hard to hit them without getting hurt yourself.
Advanced Strategies: Don't try to attack Nippers from below. If you smash a brick with a Nipper Plant on top of it, the Nipper will just fall right on your head!

Attack Pattern: They may start out as spores - where they land pops up a Nipper. He can hop around, and jump up to attack you.
Basic Fighting Strategies: Any attack will work on them, even stomping!
Advanced Strategies: Eat them. You'll get an egg, and it's easy to do. Note that you will not get eggs for eating Nipper Spores, although sometimes this is safer than letting them land, if there are many of them.

Attack Pattern: I think Nipper Plants are always stationary in this game, except for jumping. They don't "walk" around, in other words. If one gets you, you'll lose a coin.
Basic Fighting Strategies: You never actually fight Chompweeds; you just avoid them. It's best to avoid them at all costs, even if you have to fight another enemy to do so, because they'll take your coins, and give you nothing. A fight with a Piranha Plant will cost HP, but you earn experience and coins. If you HP is low, you might consider taking the Nipper instead.
Advanced Strategies: There aren't any - just stay away.

Attack Pattern: They may start out as spores, and when they land, they'll grow into Nipper Plants. They can hop around, and should be able to jump up to attack you, but to be honest, I don't remember if they can.
Basic Fighting Strategies: It looks like all attacks are supposed to work on them in Yoshi's Story, but you may want to avoid stomping anyway.
Advanced Strategies: Don't try to intercept them when they're in spore form, unless you have lots of eggs. Eating them will cost you petals - but will give you an egg, if you really need one. Eating them after they land is your best choice - it earns you some petals and an egg.