I feel like I'm missing the point of sky hunters. They're fine for picking off archers and siege engines and air-to-air is something I get, but past that any match up I can make is *at best* a 50/50 and generally skews harshly towards flyer casualties.

Meanwhile bombardiers consistently fail to so much as make a dent in the enemy. I get that it's that way because they get pot shots in on units that can't hit them, but anything else I can field will contribute more overall.

Besides that, the enemy fields stronger sky hunters than you starting at the second continent. It's barely worth fighting them 2 on 1 and generally archers or Malric are the real answer. It just seems like a waste to dedicate tons of resources buying, researching and upgrading very expensive units that can't actually contest the enemy.

Exactly.
I really don't know who's idea was to set this myth that you should invest in Sky Hunters and it is a must.
There is a ton of other really cheesy strats for army composition, that really makes you unstoppable.
But not Sky Hunters.

They work great with magic crossbows. I arm my sky hunters with them. And theres usually some vulnerable unit that I can use them on like cavalry or siege. Also they're great for mopping up those understrength units.

In my first playthrough I'm on the Kalador island and I got something in the region of 8 skyhunters. I tend to clear the map with them and my land units just make a show of marching towards objectives.

Hello there !

Well, for a start, it seems useful to remind that:

1) You're mentioning the second continent, but also Malric, so I guess you're writing about the early game phase while playing with Calis. It's true that even Flying Monkeys can be a bit of a pain at that point, mostly because of their Magic attack rating which skewers most units' armor by 25%. Should you play with Krell (and his Magical units) or Mordra (and her wonderful Flying Snakes ^^), you'd feel less of a gap in early aerial duals, even in Hard mode...

2) Aelcar doesn't necessarily field Sky Hunters of a higher grade than you... It really depends on your research choices. A Grade advantage goes a long way with Sky Hunters. After that, it's true that most early Mortal units are a tad underpowered or at least not better than your enemy's counterparts, but you shouldn't really notice the difference if you've been grooming them well enough. The manual's right about those... You really don't need that much of them if you can't maintain a good level of experience. Two or three higher level Sky Hunters do a far better job than twice that number if they're still at level 0 or 1.

3) It's hard to base observations on that sole early game phase. For example, even those Mortal Sky Hunters will suddenly feel a lot easier to use once they've reached Grade 4 or 5, because of their Heroic ability - which allows them to always maintain their (15) maximum Attack rating. Before that, yes, a few wounds and they're already far less powerful. On the contrary, Malric, even if he remains useful throughout the game, loses a lot of his interest during the last phases - and even more so in Hard mode. And that's if (and only if) you're playing Calis... Otherwise, you won't have that hero and, therefore, won't even have the luxury of being able to use him to soak aerial attacks. You won't find Valira as durable for that purpose...

Now, that said, you've more or less already figured out the Sky Hunters' true usefulnes and... it's completely within the guidelines of the manual ^^ ! You have to use them patiently, from an early point of the game in order to earn that precious XP, by finishing off stragglers or wounded targets, diving on Siege units or Bombardiers - Archers are riskier targets -, gathering several of them (a minimum of three, as for any other type) on a lone unit to obtain that +4 bonus - no need to attack with the three required to get it. It's even sometimes more interesting to park three Sky Hunters near an enemy one and only attack with the last of the three. Just to inflict damage while avoiding casualties. Patience is (really) required there, but it pays off in the end, especially with Mortal units and later upgrades.
You shouldn't try to use them to contest any enemy units head-on with Sky Hunters. They're simply not designed for that purpose - use Heavy Infantry or Cavalry for that -, though Krell's Phoenix Hawks can more or less become baseline troops if you have enough of them - and that's quite a "cheesy strat" indeed. Units' usefulness (and gameplay anyway) in Fantasy General comes from associations and Sky Hunters are mostly interesting for maintaining aerial superiority, which is a keypoint in PvP (PlayByMail) games. The first player who can't respond anymore to aerial attacks usually loses... But even in the campaign, they're great units when used correctly, because of their movement (unhindered) speed - which blends nicely with Calis armies, if you fancy Cavalry -, great vision & recon value, which allows you to scout any part of the map with ease, slaughter pesky Siege units in a flash or force the AI to retreat (or sometimes engage) by lying them in bait somewhere.
Now, with Calis, you can also play with Heavy Cavalry units equiped with Crossbows ^^ - works well enough, though some players consider this cheating ! - or use Light Cavalry (and Cloaks of Hiding) to do your recon. You can also, indeed, double down on Archers or Siege Engines, but they're so slow that you'll really have trouble maintaining your army's cohesion throughout a mission... But once difficulty ramps up - in Hard mode or even in Medium, if your strategy's not efficient enough -, it's just way easier to use Sky Hunters. I mean, with Calis, any mission is more or less over in 3 or 4 turns with enough planification: the main (initial) fight is usually over at that point and if you've positioned your ground recon units all around the map, you'll prevent the AI from recruting reinforcements. Which means it's over, save for a bit of cleanup, Shrine exploration, etc. And that's simply impossible to achieve (that fast) with Archers or Siege Engines if you couldn't force the main fight to occur close enough to your starting point or if you had to compose with a lot of Rough terrain.
Kharille is right above: you can, at least in Medium mode, pretty much clean up a map with aerial units while the rest of your army gathers towards its keypoints. Bombardiers, while not popular in PvP for several reasons, are very handy during the campaign in such occasions... and they definitely should be much more efficient than what you seem to suggest. Maybe you had only level 0 or 1 units ? Or were just dishearted by poor luck ? For they do get a +3 bonus against Cavalry units and work usually very well, even against Infantry, when softening troops before an assault is important. Just don't pit them against Archers or retaliating units all the time and you should have great results ! Even a loosy Bronze Glider can burst much more expensive units (during the early game) if you've protected it well enough until it earns a few levels !
As for Lipatov... Well, there are indeed lots of methods to build a strong unstoppable (campaign) army - since PBM games are a completely different beast - and, in Medium mode, pretty much anything will work out in the end if you have a bit of patience and don't rush in. But, objectively, you simply can't pretend Sky Hunters are useless. And I'm not even limitating the subject to Phoenix Hawks or Shadow Dragons ^^...

Good luck with your army !

So flying monkeys have magic attack...that explains why they seemed SO powerful. My sky hunters at the same level take a massive beating from them. It's so frustrating.

Troubles happen exactly in the situation you've described, that is when you have roughly similar numbers of Sky Hunters than Aelcar, of the same Grade and the same level of experience. Then, yes, you're beat or taking heavy casulties.
In order to avoid that, try:
1) To maintain higher numbers at the same place. Attacking and defending "en masse" is always a good tactic. Even if you can't surround them, that will allow you to distribute the damage among your units more efficiently. Also, the +4 bonus to their Attack ratings shouldn't be underestimated.
2) To let your rookies attack first, to soak a bit of damage at a low (experience-wise) cost. Your veterans should only come in once you're more or less guaranteed low cost assaults or low cost finishing blows.
3) To soften superior enemies from afar. Anything goes... Archers, Siege Engines, but also any spells. A Staff of Wind, a Storm Staff or a Wand of Disease can help a lot.
4) To equip your evenly-matched units with appropriate items. Magic weapons help a lot - usually more, from my experience, that protection items (as far as Sky Hunters go) -, but if you have stumbled upon an Amulet of Magic Resistance, then you're golden. Keeping a single Sky Hunter equiped with it, as a specialized counter against Magical units - since he'll get +150% to his Armor rating against them -, will help you a lot. Just use him as some sort of tank each time a unit dealing Magic-type damage bothers you...
5) As a last resort, if you really can't deal with them or if they cost you too much, try to simply remove from their vicinity any vulnerable unit you care about. Leaving only or mostly Infantry or Cavalry units around, for example, will sometimes prompt the AI to attack those in a desperate manner - for it will usually lose a lot in the process. It's what people who try to play without Sky Hunters hope to achieve.

Aelcar doesn't field that much aerial units, honestly. You'll rarely face more than 2 or 3 at once, even taking in account Bombardiers, so you shouldn't be having a lot of trouble as long as you don't attack recklessly with anyone. His spells will probably bother you more than them...

I can think about three tips to help you :

1) There's a classic way to deal with Aelcar's spells which is to buy a basic (Grade 0 or 1) Sky Hunter for the sole purpose of attracting Whirlwind damage. Just like a metal rod during a storm ^^... You don' care about that unit, won't upgrade it and aren't seriously trying to do much with it : it's just there to stay in Aelcar's sight - it needs to be constantly within in vision radius - in order to draw as much fire as possible. Just make sure it's out of his Sky Hunters' reach though. You don't want to lose this precious punching bag ^^... This won't work in 100 % of cases though, as Aelcar enjoys switching targets from time to time, but it can help a lot. Against him... and the Shadow Lord eventually ^^'.

2) There's another small bit of information which can help you... The AI, regardless of which general you'll face, seems to consider its targets from left to right (considering your army roster screen). It's not really a question of numbers - it won't hit the 1st of the Green Dragons before the 13th of the Green Dragons obviously (names mean nothing to it) -, but merely of veterancy. Your first and oldest unit alive will draw its attention a bit more. In practice, this isn't very noticeable during ground combat, since there are so many other factors the AI considers that, in the end, you can't really take advantage of that part. But, in aerial combat, since there aren't that many units and spells just, well, hit one of those unlucky few, it's definetely something you'll want to know. You'll notice that Whirlwind hits usually that oldest unit or second oldest unit a lot more... and, when it's not that one, it will then often fall on your weakest unit (the opposite side of the roster screen). Those in between are very rarely hit by spells... This can be used to your advantage if you happen to find an Amulet of Magic Resistance. Just give it to that oldest unit and you'll save yourself a lot of trouble... on top of having an efficient tank to face Magical Sky Hunters.

3) Yes, you can always try on Easy mode or perhaps even better : select a "Custom" one for your needs. There are two markers : Gold and XP. Give the AI a bit less Gold for example - this helps all game long, by diminishing the number of reinforcements the AI will be able to buy - or a bit less XP - which doesn't change the XP level of any map's starting units, but makes sure all reinforcements will remain close to "0", as your own rookies. This helps especially in longer campaigns...

Don't give up ^^ ! It's rarely a great game... and don't forget to check the *.pdf manual at first. Like for Shadow of the Horned Rat, SSI made sure to include a lot of precious information about the units' stats, spells, magical items, etc.

Cheers !