Annoying Video Game Helper: Ralph. He'll give hints, but more often he just nags Link for wasting time helping other people instead of trying to save Nayru.
Anti-Climax Boss: Ganon. He's slow and predictable, and he doesn't have a second/third form like the two vanilla final bosses and the boss that comes before him. Some of it is justified by the fact Twinrova couldn't offer the proper sacrifice for his mortal vessel, making him a mindless beast and likely less powerful than he ought to be, but it's still a bit jarring for the former King of Evil.
Awesome Music: For a handheld game, the final boss music for both games counts. Onox, with his dragon/wyvern form, arguably pulls it off better.
The Tarm Ruins from Seasons is a surprisingly mellow and melancholy song that many people remember.
Meanwhile, Dancing Dragon Dungeon, also from Seasons, is just so damn funky.
Breather Boss: Plasmarine, boss of Jabu-Jabu's Belly in Ages. Really easy to dodge, has only two attacks, and one of them is incredibly slow-moving. Considering that level's reputation among the fandom, it also counts as a Hard Level Easy Boss.
The Black Tower in Ages isn't exactly an awesome dungeon, but it is a dungeon with a couple of puzzles and a long path. Onox's Castle in Seasons, on the other hand, is barely a dungeon at all. The level consists of three wide-open rooms where the path forward only opens if you kill all the enemies in the room first, and they're the same normal enemies you've seen all game. Walk up, kill the enemies, walk up, kill the second batch of enemies, walk up, beat Facade (a very easy miniboss), walk up to find Onox's room. The fight with Onox will likely take far longer than the time it takes to get through his castle.
There is also the Ancient Tomb, the eighth dungeon of Ages. Its dungeon item is... an upgraded power bracelet, possibly the most underwhelming item in the game. The dungeon itself requires quite a bit of meandering and backtracking, due to being based on a central location requiring four key items.
Evil is Sexy: Veran.◊ As you can clearly see, Veran reads like a scrolling laundry list of kinks, and then some. Even two of her One-Winged Angel forms (her true appearance as a fairy and her beetle transformation) are Cute Monster Girls, although they do veer a bit toward the creepy side.
Game Breaker: The Red Ring in Seasons doubles all sword damage. This makes any normal attack a Spin Attack and Spin Attacks do quadruple normal damage. With the Noble Sword, Spin Attacks reach 8 power, and the Master Sword in a linked game raises that to 12 power. Even the final bosses of the games will die in three or four spin attacks at that rate. This also explains why so many late game bosses and minibosses are immune to sword strikes or are Puzzle Bosses.
Goddamn Bats: Keeses are more obnoxious in this incarnation than in most others. Especially the flaming varieties.
The second boss from Ages, the Head Thwomp, is this if you don't know the trick. You must sit on slow moving platforms that rotate above his head so you can drop bombs into him, making him spin around. However, you have to make him stop on the red head to actually damage him, everything else gets an attack. There's a precise timing to it (throw the bomb when his face turns purple), and you can eliminate a lot of guesswork by tossing bombs from the edge of the solid platforms up top, but it's still annoying.
Twinrova's first form in a linked game. You have to bat the projectiles from one sister into the other, but they can fling projectiles from off-screen, they move quickly in unpredictable patterns, and you can't easily control the angle you deflect them at. Thus, the fight mostly involves standing against a wall swinging your sword at the projectiles hoping the right sister feels like moving into the path of it in time to get hit.
Marathon Level: The Ancient Ruins from Seasons are a strong contender for the longest level in a handheld Zelda game. It doesn't help that Manhandla, the boss, is considered Seasons' That One Boss.
The two Pieces of Heart you get from a Gasha Tree and Maple. It is completely random when these pop up, so prepare to spend a long time trying to get those. Worse yet, depending on where you run into Maple, there's a chance the Piece of Heart can end up stuck in a tree or rock wall, where you can't grab it. The trick to the Gasha heart piece is that only some spots can give it up at all, making it a Guide Dang It instead. Maple is still just as aggravating, but both of these heart pieces can be save scummed, provided you manage to snatch Maple's before she gets to it first, anyway.
Swimming in Ages after you get the Mermaid Suit. You have to mash the D-pad for an entire dungeon. To counterbalance that, it's fast (much faster than mashing A with the flippers) and lets you use your items.
The Blue Cucco segments en route to Dancing Dragon Dungeon in Seasons are enough to make you wish for a Game Boy with a turbo button.
Take That, Scrappy!: Ricky can't stand to be around the creepy man-child, Tingle. The kangaroo will leave Link if they go anywhere near him.
Smog, also in Ages, for being a particularly frustrating Puzzle Boss. What doesn't help are the projectiles he shoots that can easily deal a great amount of damage if you're not careful.
The Ancient Ruins boss Manhandla, a giant Venus flytrap that shoots fireballs. Sounds easy enough, except that: you need to take out the heads with the boomerang, the heads are only vulnerable when they're shooting at you, the boomerang averts the "precise" part of Precision-Guided Boomerang when you're trying to guide it around (the heads are on all four sides), the boss gets faster with every head destroyed, you use the same buttons to move as to control the boomerang (making you a sitting duck), and, adding insult to injury, there are conveyor belts on the floor that pull you into the boss if you step on them (see: same buttons for movement and boomerang). Good thing you found that Quicksand Ring a while back, right?
The Ancient Tomb boss Ramrock is a long and complicated Puzzle Boss requiring the use of many different items and strategies, many of which are very unclear. For instance, in its first two forms, it is immune to the seed shooter, yet in its third form this inexplicably becomes its only weakness. You will basically only discover this if you flail around trying absolutely everything, but why on Earth would you use the thing you've already established is useless? You are also supposed to throw bombs between its hands in its second form, but the window (in both time and space) is incredibly narrow, so it's easy to throw a bomb only for it to prove ineffective, at which point you might reasonably assume that you're supposed to do something else.
Veran's spider form can be frustrating. The only way to make it vulnerable is to detonate a bomb on it. There is a respawning bomb drop in the arena, which is a pretty big hint... but it also has an attack where it tries to catch you on silk and reel you in, making Feed It a Bomb a reasonable assumption. This will, of course, mean you will be detonating the bombs away from Veran, making it difficult to discover the weakness.
The Goron dancing minigame in Ages, because it's so easy to screw up the timing. What makes it worse is that it's mandatory to complete the game. Not only that, but doing the dancing minigame in the Past before the appropriate time will not give you the key to the Mermaid's Cave in the Past, and you'll need to do it again when the time actually comes.
Jabu-Jabu's Belly, seventh dungeon in Ages. It's a goddamn maze in there, to solve certain puzzles you have to navigate and backtrack through a dozen times, and being as it's inside a giant fish at the bottom of the ocean, you have to use the Mermaid Suit to get around.
The Ancient Ruins from Seasons is almost hilariously dickish in its obvious antagonism toward the player and willingness to break Zelda conventions. It's an already large level which contains multiple pointless rooms full of enemies and hazards. There's a hallway trap unique to the entire series that will send Link to an instant game over unless the player can speed through an obstacle course with almost perfect timing. One puzzle involves two randomized switches; one allows further progress while the other drops snakes on Link's head. The experience concludes with a particularly annoying boss. The fact that it immediately follows the run through Tarm Ruins and the Lost Woods doesn't help.
The eighth dungeon from Ages has an underwater sequence with quicksands. One particularly tricky part is almost impossible without the quicksand ring.
The Hero's Cave in a linked game. In an unlinked game, it's just a short dungeon in Seasons that you go through to first get your sword, and it doesn't even exist in Ages, but in the linked games, it's 21 rooms long in Seasons and 15 in Ages and in both cases you need to have the equipment from the 7th dungeon in order to clear it.
The second-to-last puzzle in Seasons is hair-pullingly hard, because you need to perform a very precise boomerang throw to hit a switch. And the boomerang is FAST, which mean you need a hell lot of reflexes to pull it off. However, you can circumvent that puzzle by using Pegasus seeds to control the return path of the boomerang in such a way that it goes through the blocks and hits the switch on the way back. Bombchus work too.
Then there's the dice puzzle in Ages. You have to push a colored die over three color tiles in a room filled with lava. You can cool it down by pulling a lever, giving you only a few seconds to push the die from one safe area to the next. If the lava starts to boil again while you roll the die over it, you lose it and have to exit the room and start over from the beginning. To make things worse, you access that room through a warp vortex, and if you fall into the lava, when you re-spawn on top of the vortex, it immediately warps you out of the room, forcing you to start over even if you didn't lose the die. There really isn't much room for mistakes.
A few of the linked game mini-games can be this. With Seasons being the first game you beat, cutting grass with the Magic Boomerang in just 3 throws. With Ages as the first, the one that stands out is doing the sword batting cage mini game WITH THE BIGGORON SWORD.
The Goron Dance on Platinum level requires up to 10 precisely timed button presses, and you have to do them perfect all eight times in order to get the Bomber's Ring, and there is no other way in either game to get it. The 3DS Virtual Console release inadvertently makes this much easier by allowing the player to make restore points during the dance between rounds, so you can just save scum until you nail it.
Both Veran and Onox were interesting villains with unique powers, cool character designs, and creative methods. However, the Big Bad turns out to be Twinrova, with Ganon as the Greater-Scope Villain and True Final Boss. Onox especially gets it bad. Unlike Veran, who has plenty of personality, Onox is a Flat Character because we don't see him as often.
Farore thanks to being Demoted to Extra during the development. She's the third Oracle and has her own artwork, but she has no role in the story and only exists to get items by giving to her linking passwords. This is especially jarring when the goddess Farore is associated with courage, Link's virtue.
Viewer Gender Confusion: Ricky being a male kangaroo with a pouch didn't just confuse the fans. The Nintendo Power writers called Ricky a "he/him" in their first preview only to switch to "she/her" in the following preview, likely because the Fridge Logic set in. They went back to "he/him" during their mini-guide, presumably because they had gotten their hands on the game at that point and found out Ricky really was a guy. Zelda.com also originally referred to Ricky as a female, though given its horrid reputation, that's not exactly surprising.