Alright, I've played this for an hour or two now, and I've got a lot to say.
It starts off really well, and I can tell from the beginning that you definitely know how to use events, scripts, and maps properly. The first few interactions with the villain were enjoyable, and having a talking cat is a nice twist on an RPG. Getting to choose your class was good, and you went to the extra mile of making their graphics change afterwards! The grammar was proper, the formatting went well, the scene control and pacing was nice, all the maps, and even the idea seemed worthwhile!
So, what happened to it all -
I'm sure you already know the main culprit. Random encounters. When I posted about this earlier, I would have never guessed the random encounters were this obstructive to your game. Now, here's the big statement I need to make before really diving into this: nobody likes random encounter, but you can have them in your game.
All those battles do almost 90% of the time is hinder your character, they're made as an obstacle to slow you down, and at the same time give you opportunities to level up. You're not going to enjoy a random encounter if you had one a few steps ago, or if you're about to reach a door, or a chest. Every time the player has to start a battle they don't expect, a ton of momentum is lost in the game. A random encounter, to a player, is a bad thing almost all the time, so it's rare that they'd enjoy it. The only game I think of when I think of random encounters is Pokemon, and Pokemon does random encounters so well. Pokemon has a balanced amount of encounters, caves aren't too long and bushes can mostly be avoided. Plus, you've got so many Pokemon to level up and evolve, that you're constantly getting rewards, you only fight one wild Pokemon so they're fast, AND you can even catch the opponent! So what you need, is less random encounters, less, less, less.
While there were rewards as well, they definitely didn't help motivate me. The majority of rewards from what I recall were recovery items, gold, and ice key shards. Some of the chests I had to go out of my way to get, and all that meant was more random encounters, which I'd gotten very tired of after the first floor of the ice dungeon. The maps suited the idea, they had a really nice general layout, maybe a few stairs and changing depths would make them better, but overall I don't think I need to complain about them. However, there were definitely too many of them. Or, more likely, there were once again, too many random encounters. I kept getting up higher floors in the ice dungeon and I just wanted to be on the last one already.
Finally, the big solutions to your random encounter problem:
1. Divide the amount of random encounters by about 4.
2. Use region random encounters instead, and find a way to section off the areas visually. This could be done with lighting, darker floor tiles, just find a way if you can. Even if you don't have any visual indicator, less regions with encounters would definitely benefit your game.
3. Less floors.
4. Create proper events and puzzles through the dungeon, like mini bosses, shops, characters you can interact with, and meaningful chest rewards. If you do make puzzles, try not to make random encounters get in the way of them.
5. Remove random encounters completely, and put events on the map instead.
If I were you, I'd do 2, 3 and 4. 1 is an immediate fix, but even then, if that's the only one you do, I'm not sure diving it by 4 would even be enough. Otherwise, the rates would be good if you did 2, 3 and 4 all at once. Doing 5 might be cool, but it's a lot more effort and it'd mean you'd need sprites for every enemy encounter, unless you did shadows or something. 2, 3 and 4 sound like they'd really suit your game though! If you can figure out a way to get nice, balanced regions, the player won't feel like walking around is always a chore. Less floors would be good too, the first dungeon wasn't too bad because the maps were smaller (I think), but the second dungeon was absolutely absurd. You can't put 9 floors between the player and a boss fight. There needs to be stuff in between, the only way you could have a 9 floor dungeon that was enjoyable was if it was full of events and interactions that keep the player going. One of the things that upset me a lot was the lack of ice floor puzzles in those 9 floors. Those are so much fun and are a great break from repetitive grinding and battles.
That problem is the biggest, and it really, really needs to be fixed. I think there are a dozen of battlers there, but adding more and more battlers isn't the option. A couple of times I encountered singular enemies which were way stronger than most and I got excited for a bit because I thought there was something special about them, but I felt 0 reward after battling them and figured they were the same as any other monster.
Smaller problems are, balancing. Magic definitely seems a bit overpowered, although that might've just been because I had a spell blade and a sage, so I might not have had any real physical damage class. I think given what the game is, it's still relatively well balanced. You should make sure mage classes start off with some kind of magical ability, so they're not using their fists at the start. The cat being a healer was a great idea. Personally, I think the cost for healing is too low, but since there are so many battles, you end up needing that much mana. The battle system is very bland and basic, having access to a lot of classes and a proper party kind of makes up for it. You can use it how you are, but it might also be worth taking a look at different plugins you can use to improve battling. It seemed like the first boss fight took a long time, however that could be okay, the pacing was very slow due to the encounters, so having a long boss fight wasn't a big deal.
What I think, is that you've got a lot of potential in this games story. More interactions, fun ones, cool ones, any of that would be great, since the start made me want more of that. Since it's a dungeon game, you'll be a bit limited for interactions, think of ways to get around that. Think of things to put in the dungeons that the characters can interact with. Put history into the dungeons, make them seem alive, rather than just being ice for the sake of ice. And also, put an escape staircase on the first floor so that you can leave it if you're dumb like me and accidentally go back into it, because that's the first thing I did after completely the ice dungeon. (I quit the game at that part.

)
TL;DR
less random encounters
- region encounters
- puzzles
- events
- better rewards
- less floors
think of a way to spice up combat
use all the character potential you've got
don't teleport me back to the beginning of that hell-hole ever again

and most importantly, do your best!
As I said before, your introduction was fun and I wanted things that built on that. So keep me updated on the game, and feel free to chat if you need any help/advice, good luck!