=Rot heap boss: The Aggregate Zero=
There's a lot of enemies. The boss has 4 subparts, and is basically immune to damage until the subparts are gone, so you have to take them down first. The boss will initially spend TP on healing and reviving its subparts, so it's a DPS race.
Being wet, the AoE fire attack won't do much, but the AoE thunder attack(if you have learned it) will work very well. Otherwise, it's a matter of beating down the mook enemies it spawns with, then the subparts, and finally the boss' main body.
Aside from that this boss should be more or less similar to the previous bosses you meet - beware of the ailments they inflict and incoming powerful attacks, and you'll be fine.
=Forgotten village boss: Thousand Faces=
Remember the gimmick from the Amaryllis boss? Yeah, it's here again. Multiple fake bodies and one main body, shuffling each turn. The same countermeasures apply, but since the fake bodies now have TPMAX moves, using AoE attacks is a VERY bad idea.
Speaking of which, both the boss and fake bodies only have attacks used by this stage's enemies; the same precautionary measures apply. Just burst down the boss while dodging/defending against the fakes' attacks, and you should be fine.
Come phase 2, the boss will summon even more masks (AoE attacks is an even worse idea now...), but there's nothing new.
At phase 3, all the fakes will die out immediately (thankfully) but the main body now gains a bind move he'll also use on you straightaway, but if you can handle that he's not different than the other bosses.
=Sky garden boss: The Strongest Taimamiko=
Hey, it's her! From the dev's previous game! And she's not on our side. Oh boy.
First off, her title has grounds. She's RIDICULOUSLY strong, and has speed and skill to back it up. If you get hit, you're in for a world of hurt. Thankfully, you have two tanky oni on your side, who are capable of dishing out the damage on their own, and attract most of the heavy fire. Because of the boss' relentless onslaught however, they'll need some help taking it, which is where you come in with healing and revival spells and items. The oni have enormous HP scores, so use percentage-based heals such as the expensive full heal+ailment cure+revival spell. Just keep your party healed up, and the boss'll go down sooner or later.
=Undersea base boss: The UFO Gather=
First things first, the boss is utterly invulnerable at first. Nothing will work no matter how hard you try. Just do whatever you can to keep yourself from getting annihilated until Mayuko mentions the alien managing the barrier on that console up top... And then run away from the battle. No, really.
Backtrack to a side path in the room, walk over to that alien managing the barrier, beat him down, and then interact with the console to blow it up and power down the barrier. Now get back to the boss fight.
The boss itself won't do anything other than summon UFOs and such for the first part of the fight, so feel free to burst the UFOs down and then focus on the boss. The "regular" UFOs are pretty normal enemies, while the "heavy" metal-plated combat UFOs are tough but weak to armor-piercing attacks such as your 22TP move.
The boss will start attacking later in the fight with powerful MP-draining light attacks. Equip light resistance accessories to counter this, and continue on as you did before; it can summon Mecha-Takoras too later on but you should be able to handle them.
=Golden pyramid boss: The Faceless King=
The first thing you should notice is that the main body's 100TP move is an unblockable, undodgeable petrifying gaze that turns you into gold. Since he starts with it. It only lasts for a short time, so you should be fine as long as you start the fight with full HP and decent equipment.
Aside from the boss, there's also a red hand, which attacks with powerful physical attacks, and a blue hand, which attacks with magical attacks (beware of the faint ailment, caused by thunder spells!). As usual, your priority is to burst down the hands, and leave the boss for last.
As for how to deal with the petrifying gaze, well, you equip the ink sunglasses (occasionally dropped by Mecha-Takoras, you probably have a couple of them by now) to intentionally blind yourself with ink, at least one turn before the TPMAX warning (since the ink-blind only starts to take effect the turn after you equip it). As long as you're ink-blinded, you're immune to the gaze.
When he hits phase 2, he'll start attacking normally alongside his hands.
When he hits phase 3, he'll then revive his hands as golden versions instead of his normal ones. The golden hands are invincible, so take no detours and focus solely on the boss.