Bruton: The best thing to do is use the Lightning Enhancement on Ark, then sit in a corner and attack. You have three at the start of the game, so if you nab the ones Vanrose and Doug are carrying, you will most likely have enough to last the fight (if you're skilled or lucky, the first one is all you need but extras are always a nice thing). Once you get to the stairs leading to the boss floor, use one of your enhancements and go down (this will make sure that you don't have to reapply it if by some chance you still lose). Equip the remaining two Lightnings in your Quick Inventory, then fill the remaining three slots with whatever you like (I tend to go for Potion As, just in case of injury from being attacked). Once Genox releases the monster, run off to a corner and start swinging your sword rapidly; it will eventually run into the beams and take damage. Just be careful to watch for stray fireballs and the monster's charges, they can do big damage. If ever you're hit, have Ark use another Lightning after getting safely away from where Bruton is standing.
Moonflow & Sanfraw: No preparations are necessary, but I would advise taking out the red flower (Sanfraw) first. Run around the battlefield, hitting it when it charges, and it'll slowly go down. You'll occasionally be lucky, and Moonflow will hit his companion with a stray fireball, doing a little bit of damage to it. Once Sanfraw goes down, then rush over to kill Moonflow, avoiding the fireballs as you do so (that's the most likely thing to kill you unless you don't dodge the charges in time). I found this one easier if I was constantly on the move unless attacking.
Fire Dragon: Really no strategy is needed. Kill two heads, grab blue sword, slash big Dragon with said sword while avoiding fireballs. Keep out of the middle (unless changing which side to attack on or running for the swords, but you don't want to attack from there) to avoid big hot flame breath, and run forward whenever wind blows throughout the battlefield. The tail at the back does nothing, so you can ignore it.
Fallayga: No real strategy required. Just avoid it as its running around the room, striking it when it stands still for a moment.
Focjabe: It slowly begins gathering more dust balls around it, so try to attack when there's an opening. When it charges, dodge the attack and use that time to strike back. If there's too many dustballs for you to get around, try dodging some more and eventually it'll return to zero and start again.
Belton: Essentially, this is a Cage Match with electrified walls, so don't touch the swords around the battlefield. Because of the low movement area, you simply have to hack at its body, hoping to kill it before it kills you.
Farlay: One of the game's easiest bosses if you're patient. Farlay will throw several things at you: a small glowing ball that splits into fireballs when attacked, fireballs appearing around the room, meteors and rocks. The rocks can be hit back at him, causing the boss some damage (think the wizard in A Link to the Past and his energy ball deflection). Also, when the meteors fall and stay for a bit, then you can destroy them, sending rocks around the room and hopefully hitting Farlay in the process. But, run from the ones that continuously fall. And if a pair of meteors fall far from where you are at the moment, then don't go for them; they'll probably explode before you can finish.
Fallayia: If you're lucky, when the two heads attack you they will both be in range of the sword at the same time. Stand near one, attacking it and when the other comes at you, you'll be able to get both. Once the first is dead, the second should follow in short order.
Keckfraw: Keep running around the battlefield, feinting in the opposite direction when it charges (the monster doesn't seem to know how to change its direction mid-attack). Before the black smoke-like things surround it, rush in and get a hit or two off, then run again to avoid the smoke. Lather, rinse, repeat and you'll kill it.
Zikjabel: Avoidance until after a charge, much like the previous boss, seems to be the best tactic I can think of. And try your hardest not to get hit by the fairydust it likes to shoot out at you. I find it very ironic that the bosses of the past two dungeons, both containing one member of a couple, have such similar patterns done differently. Though this one is waaaaaay harder, because the energy it shoots out doesn't go away as quickly and follows you around.
Falcken A/B/C: AKA Doomtrain Falcken. You'll be on a battlefield consisting of several intersecting railroad tracks, lights at every intersection and nothing but darkness under the tracks. Stand at an intersection and, using the lights, figure out which way Falcken is coming from, then get off that track and hit from the side. Hopefully, you won't get the luck of having him come from both directions and not be able to make it to a safe intersection in time. There are also several mini-minions thrown at you, but they're more like 2-HP annoyances (get used to it, each CIMA builder has something like that; it's your call whether to attack and kill them or simply try to dodge) that you can kill in a single shot.
Sawma: AKA Samurai Sawma. Go up to hit him, however run when he uses any of his attacks; it might take practice to dodge just right. Partway through the battle, Sawma will split into two copies, and you just have to get rid of the fake to hit the real one. I've never seen the two go so far apart, so I generally was able to damage the fake by trying both.
Genox: AKA Happy Fun Time Dragon Genox (he'd probably love a name like that). Destroy the giant crystal majesties around the battlefield, but don't take time to collect the ones they drop (you're gonna be too busy dodging attacks). That will allow Genox to be stunned when he uses his Shuriken attack. The Stunned!Genox is the easiest to hit, however he seems to be more defended than if you get a hit off against Shuriken!Genox or his Dragon in a cloud form. But it's harder to hit those two forms due to the constant attacks so it's your call.
He starts the battle in his cloud, shooting energy balls at you, but turns into the shuriken partway through (usually you have time to destroy the Majesties first, but sometimes you don't). While he's in the cloud, running and destroying the Majesties is first priority (though some might want to take the risk to charge him for an attack...it took an accident for me to realize he was vulnerable in this form because it's so hard to do). He will shoot balls of energy off at you, and eventually change into a shuriken and charge you. Dodge when he flies at you (harder than it sounds), possibly get a hit off when he comes by if you're daring enough and when you hear the whistle signaling he's stunned you should rush to attack before he changes back. Eventually, he will return to his cloud and restore the Majesties, so repeat the process till he dies.
Elvira: AKA Cindy Campbell's Shopping Buddy (another spider woman boss, from Red's Quest in SaGa Frontier). She starts running around the battlefield, and you have to rush up at her and attack. Sometimes, she shoots webs down at you, which will trap you for a few moments as you struggle to get out. Dodge them, but be careful of her fireball barrier (you have to get around it to even think about damaging her). When she runs out of HP, you're still not done. Elvira takes to the trees, coming down at you from her web. Here, you have to dodge her attacks and hit her back, as well as the occasional stampede of mini-spiders. However, if you have enough Potions left, sometimes getting stuck in her web will allow you to hit her easier, as long as you keep attacking. Not only won't you have to chase after her (as she'll come down at you now), but a fully upgraded Ark can do more damage than she can.
Brutray: AKA Cage Match on the Loose! Fought by Vanrose, it's a recoloring of Bruton and Belton. It's a simple boss, just dodge the Eyes it tosses at you and get in close to attack. Compound that by the fact that Vanrose is stronger than Ark at comparable upgrade levels, with the same defense, and you've got a pretty easy fight.
Frawdia: AKA Isn't This the Fourth Flower Boss!? Fought by Doug, if you can't tell it's a recoloring of the three previous flowers you beat. It turns invisible, then appears randomly around the room, shooting things at you. There's two ways to beat it: A) run around and hope you luck into where it's standing before it vanishes again or B) stand in the middle and follow the attacks back to the source. After it attacks and its beams return to it, Frawdia vanishes again to repeat the process.
Arcjabel: AKA A Knight That Plays With Rick's Head! Fought by Rick (duh), it's a recoloring of the monsters sent by Elvira in Cold Snow and Air Garden (minus the wings Zikjabel adorned in the latter) It alters between two forms: a giant knight and the likeness of Diana. When in Diana's form, it can be damaged, showing a Trust down heart whenever you do so. When in knight form, dodge its energy balls and strike after the transformation. All in all, not too difficult a boss.
Fallaysa x 6: AKA either The Boss From Hell!! or A Giant Letdown of Six Two Headed Serpents!, mattering the day and how badly I screw up. Fought by Jean, it's similar to Fallayga in looks. Combine having to throw your weapon at them, with the sheer numbers, you are in for big trouble. At first, hitting isn't the problem...but staying alive long enough is since sometimes you can't dodge them all. If you have good aim, it only gets easier as the monster numbers dwindle, since you have more room to dodge in. If not...you substitute the being beat up problem for the issue of Jean's darn scalpels being the hardest distance weapon to aim (in my opinion, it could be due to the fact that the other three are fundamentally similar and feel the same to shoot).
Pike, Dark Mist x2, Energy Gate, Fire, Gun: AKA Pike and his Giant Machine! You start out by having to destroy each of the weapons on the machine, which are left vulnerable when he uses them to attack with the exception of the gun (it's always vulnerable, it's getting to it that's the problem). So you'll probably destroy them in different orders every time you play. Just dodge the attacks (Dark Mist is especially troubling if you don't have Poison immunity), strike at the weapons until each are defeated.
Pike then switches to assaulting you directly, tossing energy beams that remind me a lot of those rocks in the desert in Lagoon (different look, same dodging pattern). Get in between two of the beams, and try to keep yourself there (he moves around so much that you have to be in constant motion). When Pike stops for a rest, you can hit him. However, eventually he will be jumping around the battlefield at you, and you have to go at him when he's in motion. A few dives at his position (I usually had to run the gauntlet from the back of Pike's machine to the front) and he should go down. Though it seems he switches from attacking with the energy beams to dodging while shooting a back-mounted beam at different points, rather than when his HP sinks below a certain level.