Stage 4 might look threatening, but it's not too bad. The main difficulty here is navigation. Your eventual goal is to pass through the two locked doors in the dungeon, but you'll also need to find switches to reduce the smoldering purple flames in the area to nothing. Note that some flames are larger than others, and will take two switches in order to be extinguished completely, allowing your party to pass.
The enemies in this chapter are starting to become a little more dangerous, but few should pose any major threats. As you might imagine, a lot of enemies here are weak to water damage, as well as light, so characters who can exploit that will be very useful. Be careful of red gator enemies, who pack a lot of HP (500) and resistance to all physical elements, and the floating stones, who have a very high physical defense stat and pack a single-target instant death spell.
Kisume doesn't pose too much of a threat, and packs a very basic pattern - she spends a turn to charge up, then makes a basic physical attack on a party member. Most of the time this won't be so bad, but she can one-shot characters with weaker defenses, so try to use a formation that will focus her attacks on characters that can handle it. The difficulty here is more that it takes a long time to chip away that much HP - she has a resistance to Water, Fire, Light, and Dark elements, as well as a very high defense stat for this point in the game and a moderate magic defense as well, her only weakness being electrical elemental attacks. Ultimately, she's really not that dangerous; just be aware that you're in for a potentially long fight for this part of the game, and she's located in the farthest reaches of the dungeon, so be careful to check your MP reserves before going in.
Boss: Utsuho Reiuji and Rin Kaenbyou
Utsuho Reiuji's HP: 2000
Rin Kaenbyou's HP: 1500
Another double boss fight, but unlike the ones in chapter 1 and 2, both of these two have some very dangerous abilities you need to be wary of. They've both got a lot of potential to damage your characters, and both magical and physical attacks, with some minor status ailments... but also each carry condition abilities which could do some terrible things to your party if you let them. Both of these two are extremely resistant to fire and carry fire-elemental attacks, but you can exploit that by using elemental attacks and, if you've raised her enough to have them, Patchouli's elemental field effects, to weaken fire and greatly strengthen Water, which will work very well on both of them. Also note that the land effect greatly favours light magic here, so Reimu, and possibly Byakuren with Starfire, can also work just as well.
The first target you go after should be Orin. Although her damage output is generally not quite as high as Utsuho's, she packs attacks that can inflict Blind or Curse, which will put a dent in the offense of your team. More importantly, however, she has revival effects. If Utsuho falls before she does, she will simply revive Utsuho on her next turn. She can also revive your teammates if they fall in battle - in this case, they'll be stuck at 1 HP and will attack your party. This counts as a Permanent-type status, and can be removed, but the character will still be standing at 1 HP and very likely to be taken down again. She's got less HP, and a weakness to water element, so you should be able to take her down much faster than Utsuho anyway.
Once Rin is down, you can focus on taking out Utsuho. Utsuho herself packs mostly damage attacks, though she can also poison a party member when attacking. She has no magical defense, outside of her huge fire resistance, and is weak to light, so Reimu and Byakuren can deal large damage, as well as anyone using any form of magic, really - especially water, since you probably built that up taking out Orin. The difficulty with Utsuho is that she attacks fast - she'll generally be going first, excluding Last Spells. This becomes a real problem when she drops down below roughly 40% health, where she'll kick off her turn with Giga Flare, which will do roughly 300 non-elemental damage to the whole party, which is pretty much guaranteed to kill everyone. There are several ways around this - Mokou's Phoenix Rebirth commander spell can prevent the party from dying for that turn, Nitori's Hyper Camoflauge might save you (unconfirmed), Alice's defensive spells can help, Reimu could block it with her Evil Sealing Circle, Sakuya's Private Square can lock her out, or you could just plow through the latter half of Utsuho's HP in a single turn with an offensive party (Try using Sanae's Summon Takeminakata commander spell to raise the party's offense the turn you attempt this, or using Aya to manipulate the turn order).