Dark Nuts
Dark Nuts can only be damaged if they're attacked from the side or behind. It is more difficult to get behind them when there are two or three of them attacking at once. The remote bomb, an optional upgrade from Belari, provides a useful method for taking out multiple Dark Nuts. Drop a remote bomb somewhere near the center of the room where you're fighting the Dark Nuts. Circle around the room until the Dark Nuts are close to each other. They move slower than Link and have a fairly short range, so this is not very difficult. When they are all together, draw them over to the remote bomb and detonate it. The explosion should stun all of them, which gives you a chance to defeat the entire group at once.
Gyorg Pair
The Gyorg Pair is the most unusual boss fight in "The Minish Cap." It takes place as you're flying through the air, with Link using one of the Gyorg Pair as a platform. The other member of the pair flies off-screen for much of the fight, but it can still attack you. The Gyorg flies off-screen to one side or the other, and it will usually attack from this same side of the screen, which makes it easier to anticipate and avoid its attacks. You need to make clones to attack all three eyes on the red Gyorg simultaneously. Attack the eyes whenever they open to damage the boss.
Blade Brothers Prerequisites
The Blade Brothers teach Link new techniques over the course of the game, and most of the Blade Brothers have no prerequisites before they teach their technique. There are a couple of exceptions where a Blade Brother refuses to teach you (or even mention the existence of a technique) until Link fulfills a requirement. Swiftblade is the only brother that teaches multiple techniques. He teaches the first, the Spin Attack, when you meet him. You need to get the Pegasus Boots, Roc's Cape and White Sword before he teaches you the other three. Waveblade does not teach Peril Beam until Link's maximum health is at least ten hearts. Swiftblade I (a different character from Swiftblade) only teaches the Great Spin Attack after Link learns all seven of the other techniques.
Gregal and the Ghost
Gregal and the Ghost is the sidequest that earns you the Light Arrow upgrade. Gregal is the bedridden man in the Palace of Winds. All the quest requires is capturing the ghost that's hovering near Gregal in the Gust Jar. Unlike the other sidequests, you can miss this if you progress too far into the storyline. Going through the Veil Falls to the Cloud Tops makes this quest inaccessible. Don't head towards the Cloud Tops until you do this quest.