Attack Pattern: Red ones fly quickly along a straight course from the edge of the screen while gold ones (may be pink in the original NES game) dive downwards and then fly quickly straight forward.
Basic Fighting Strategies: Any of the usual attacks will kill them, but usually you will just have to dodge them.
Advanced Strategies: You can ride on a Beezo's back which might come in handy for getting to higher areas, but for the most part it's useless. When you're in an area with lots of red ones, it's best to use Mario or Toad, then you can easily do a short jump over the ones flying along the ground and you can duck under the ones flying overhead. Try to move forward at a slow pace so you have time to react to them.

Attack Pattern: In battle they mostly use special attacks, Willy Wisp will hit one character and cause medium damage, while Elegy mutes one character. They tend to run away if all the other monsters have been beaten. On the map they fly around fairly slowly, but their flight patterns are a little unpredictable.
Basic Fighting Strategies: You should mostly stick to regular attacks, they will only take one or two timed hits. In spite of what the official strategy guide says, Ice attacks don't work that well, and magic attacks are poor in general.
Advanced Strategies: You might consider using Sleepy Time on these guys, it works surprisingly well and it may put other enemies to sleep if you are lucky. Don't waste your FP on other magic attacks unless you're having a really hard time hitting them with regular attacks. These guys should be one of your earlier targets since they can mute your characters and they tend to run away.
When a Shy Away attacks, it flies towards a character, briefly pulls it's spear back, and then thrusts it at the character. Try to press A at the end of the thrust to block.