Barba has such predictable and easily avoidable attacks that you'll be more worried about falling than getting hit.
Assuming to know how to kill him, Carock is another, and if you have enough magic for the Shield spell, he goes from pretty easy to a complete joke.
Ironically, Dark Link, the final boss, mostly because how brutal the Thunderbird is (though you don't get to heal inbetween fights). The Thunderbird's attacks cause insane amounts of damage and are very difficult to avoid, plus its movement pattern and small target area make it a challenge to hit in return. Not at all helped by the fact just to damage it requires blowing half your magic bar on the Thunder spell. By contrast, Dark Link is more or less an Iron Knuckle who can jump (though not nearly as much or as high as the Bird Knights) and has more health. And he doesn't beam spam. He becomes even easier if you know the trick of positioning yourself in the far left corner on the arena.
The Red Dairas are the the first major demonstration in the game. They are found in Death Mountain on your way to get the hammer. You'll have only one heart upgrade at best and their throwing axes deal a lot of damage, even with the Shield spell up. Oh, you can't deflect their projectiles either because you get that spell after you get the raft. Even Orange Dairas are miserable to deal with because their axe can't be blocked by your shield and you won't have access to the downward thrust attack until after you've fought your way through them to get the hammer, meaning the only way to kill these guys is by jumping in for a stab, and your timing must be 100% spot-on or else they'll hit you in the process.
The appropriatelynamed Fokkas (bird knights) in the Great Palace. They do huge amounts of damage to Link (1 1/2 bars of his life meter) even at full life power, have the movable shield and shooting sword of the Iron Knuckles, and they love to take flying leaps that will invariably send them smashing right into Link. They're also quite durable. And if you beat them, for some reason the experience points gained is downright paltry (70 for a red one, 100 for a blue, contrast 150 for a blue Iron Knuckle, 200 for a blue Lizalfos. Then again, your levels really should have already been maxed out before you ever got to the Great Palace).
Ironknuckles, particularly the blue ones. The orange and red ones aren't so bad once you get used to them and get better attack power, but the blue ones never cease to be a pain. Not only do they fire Sword Beamsat an alarming rate as a response to getting hurt, but they back away from you as they're doing it, making it difficult to land hits! The mounted ones you face as the boss of the third palace and as mini-bosses in the sixth are especially infuriating as they'll retreat Behind the Black, leaving you to wait for them to show themselves!
Lizalfos in general, but especially, again, the blue ones. Orange Lizalfols are like Ironknuckles, only, the spear they use is faster than the Ironkunckle's sword. The red ones use unblockable maces. Blue ones throw unblockable maces, combining the worst traits of ironknuckles AND dairas. At least by the time you fight them you'll have learned the Reflect spell.
Mago (the fire mages who teleport constantly in the fifth palace) and Aru Lowder (the one-eyed scorpions who shoot fire out of their tails) are the kings by virtue of how defensive they are. While proper technique will let you dispatch Iron Knuckles, Dairas, Lizalfos, and Fokkas rather promptly, it's hard to deal with Mago and Aru Lowder at the same speed because they're either teleporting constantly (Mago) or can only be damaged when their eye is open (Aru Lowder). Fortunately Mago only appears in one dungeon and doesn't take many hits if your Attack is respectable (three at 6 Attack, two at 7 and 8) on top of giving a hearty 200 EXP for the trouble, and Aru Lowder are fairly rare, with only one that's strictly in your way (in the first cave in the Valley of Death, a low ceiling makes it tricky to get past), as all the others are either guarding optional EXP bags, or are in a random encounter where you can pogo over them with the downward stab and run out of the map without having to actually deal with them.
Ear Worm: The dungeon theme will stay a long time in your head.
Ensemble Darkhorse: Dark Link is surprisingly popular. Some even consider him a character in his own right and give him a personality in fanworks.
Funny Moments: At one point, Link rescues a lost child, whom he holds over his head in the same manner as all the other items he picks up. It makes for a rather amusing visual.
The two different animated head statues, Ra and Mau. (Ras are the dragon-shaped ones, Maus are the panthers). Both spawn infinitely and drain experience when touching Link. Ras double as Ledge Bats, Maus basically Zerg Rush Link.
Moas are a big enough pain in the ass in graveyards, but they also moonlight as Ledge Bats when you trek across the Valley of Death, and they have an orange variant in Temples that flies ahead of you and weeps fire down from above with infuriatingly great timing.
Any enemy that drains your XP when it hits you. They tend to respawn, as well.
Hold left and right on the D-pad (normally impossible unless you have a broken D-pad or are using a keyboard), and release. This will usually cause Link to slide off at high speed in one direction. Demonstrated to beautiful effect in this TAS (though good luck doing it this well in real-time). Note that using up and down at the same time (which one might assume would have similar effects) is not always a Good Bad Bug; used in an elevator shaft, it causes the elevator to ascend rapidly, but it can easily crash the game or put Link in an Unwinnable situation if a number of things happen. Players are advised to keep save states handy when testing it out.
The Final Boss, Dark Link, can be defeated by crouching down in the left corner of the screen and stabbing repeatedly without too much trouble. However, this boss is considered so hard that most people don't even try to beat Dark Link the proper way.
A lot of fans who discovered the series with Ocarina of Time are surprised to learn that this game was the first appearance of Dark Link as well as Volvagia (translated as Barba).
It's also the first appearance of many names from said game, though continuity wise the towns are named after them.
This game is also the first to feature a grown up version of Link. He is canonically sixteen.
It's also the first game where the Triforce of Courage appears, the triforce mark on the hand is mentioned (but unseen in game) and even the first game with the three pieces of Triforce reunited.
This was one of the first games to have a New Game+ as it's currently thought of.
Paranoia Fuel: The man in Saria who proclaims, "EYES OF GANON ARE EVERYWHERE, BE CAREFUL." Its supposed to be a hint that some villagers will turn into enemies if spoken to, but new players likely won't understand until they uncover a spy on their own.
Scrappy Mechanic: When the player continues after losing all his lives, he is sent back to the palace where Princess Zelda sleeps, meaning that Link must traverse the landscape again to go back to the dungeon (except the final dungeon). If that dungeon was far away from the starting point, then have fun trying to get back there. To make matters worse, losing all your lives not only resets Link's experience back to zero, but doesn't bring back any extra lives or experience pick-ups he obtained!
Thunderbird. Having to use a lot of magic for the Thunder Spell to start depleting its HP means that there won't be much magic left for the other spells, so the player will have to survive most of the battle by dodging the fireballs and attacking the boss's weak point.
Gooma hits very hard, and it takes plenty of hits to be defeated.
Rebonack. Blue Ironknuckles are a pain to begin with, but Rebonack has the habit of backing out of the screen where Link can't stab him.
The Great Palace qualifies even though it's the last level (and therefore held to a higher standard). If you actually even made it to this dungeon, then this palace will undoubtedly make you rage because of how complex and confusing it was. There's a particularly devious trick needed to find the bosses of the Great Palace. A section of the place has floor covered in a single layer of breakable blocks. There's a hidden warp pit one block long under one of them. Link can walk right across a pit that size without falling down it, which means the player might walk right over it and never notice.
Death Mountain, which apart from the Great Palace is the area that gives players the most trouble, and you have to pass through it very early the game. Amongst other things, it involves a maze on the overworld that's easy to get lost in, along with hordes of enemies. And once in a while in the Death Mountain caves you have to face the Red Dairas, who can rapidly throw axes which, unlike the thrown swords of the Blue Ironknuckles, can't be blocked by the shield. And this comes early enough in the game you don't have the down thrust attack and probably don't have high attack and defense levels unless you've been deliberately grinding.
They Wasted a Perfectly Good Plot: This game is a direct sequel to the original game and stars the same Link as before, but the Princess Zelda featured in this game is not the same Princess Zelda rescued by Link at the end of the previous game. Instead, she's from an earlier generation and was in an eternal sleep during the events of the first game. Assuming nothing happened to the other Zelda during the six-year Time Skip, this would mean that The Adventure of Link ends with two different Princess Zeldas awake at the same time. Remember how cool it was to find out that the Hero's Shade was the Hero of Time, directly interacting with the new Hero of Twilight and showing two Links of different generations on-screen together for the first time? It could have been potentially interesting to see how the two Zeldas interacted with one another and might have raised questions about which princess is the rightful heir to the Hyrule throne. Unfortunately, this game never acknowledged this fact, there have been no direct sequels to The Adventure of Link, and it is unlikely that any future sequels will explore this avenue.
Unfortunate Character Design: The Wizzrobe's new design looks alarmingly similar to a Ku Klux Klan member, complete with white robes, pointed hood and a red cross on its face.
Woolseyism: As usual, there are some differences between the JP and US releases.
New color palettes and tile sets for the different palaces (they all use the same gray stone pattern from Parapa Palace in the JP version).
The wandering monsters were originally little balloon things.
New, more varied music.
The bosses Carock and Volvagia are now animated instead of merely static sprites.
The addition of the classic Item Get pose (before, stabbing things to get them like with the potion was done with all items.)
There's a brand-new boss in place of a second fight with Helmethead.
For better or worse, the legendary difficulty is worse in the US. Tektites only being vulnerable to the Fire Spell (and first encountered long before you get it!) is new to the US, as is XP-draining monsters.
The amount of XP needed to level up in Japan stops increasing at 4000, not 9000, which means you're a lot tougher by the time you reach the Valley of Death and the Great Palace, which are ultra-deadly in the US. To compensate, however, you don't undergo stat reduction when you die in the US version.